The development of the deterministic nonlinear PDEs in particle physics to stochastic case
In the present work, accuracy method called, Riccati-Bernoulli Sub-ODE technique is used for solving the deterministic and stochastic case of the Phi-4 equation and the nonlinear Foam Drainage equation. Also, the control on the randomness input is studied for stability stochastic process solution.
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Published in | Results in physics Vol. 9; pp. 344 - 350 |
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Language | English |
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Elsevier B.V
01.06.2018
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Abstract | In the present work, accuracy method called, Riccati-Bernoulli Sub-ODE technique is used for solving the deterministic and stochastic case of the Phi-4 equation and the nonlinear Foam Drainage equation. Also, the control on the randomness input is studied for stability stochastic process solution. |
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AbstractList | In the present work, accuracy method called, Riccati-Bernoulli Sub-ODE technique is used for solving the deterministic and stochastic case of the Phi-4 equation and the nonlinear Foam Drainage equation. Also, the control on the randomness input is studied for stability stochastic process solution. In the present work, accuracy method called, Riccati-Bernoulli Sub-ODE technique is used for solving the deterministic and stochastic case of the Phi-4 equation and the nonlinear Foam Drainage equation. Also, the control on the randomness input is studied for stability stochastic process solution. AMS subject classifications: 35A20, 35A99, 65Z05, Keywords: Riccati-Bernoulli Sub-ODE method, Phi-4 equation, Foam Drainage equation (stochastic) traveling wave solutions, Random variable |
Author | Sohaly, M.A. Abdelrahman, Mahmoud A.E. |
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Cites_doi | 10.1007/s00521-012-0933-2 10.1186/s13662-015-0452-4 10.1016/j.chaos.2005.09.030 10.1016/S0375-9601(00)00725-8 10.4236/ojdm.2011.12009 10.1016/S0375-9601(02)01516-5 10.1119/1.17120 10.1016/j.physleta.2007.07.051 10.24297/jap.v11i3.470 10.4236/ijmnta.2015.41004 10.1002/num.20497 10.1016/S0375-9601(98)00547-7 10.1088/0031-8949/54/6/003 10.1016/j.camwa.2005.05.010 10.1016/j.rinp.2015.01.008 10.1016/j.chaos.2006.03.020 10.1016/S0960-0779(03)00265-0 10.1016/j.ajmsc.2011.08.002 10.1140/epjp/i2017-11607-5 10.1016/j.aml.2011.01.006 10.1515/IJNSNS.2010.11.12.1103 10.1016/j.chaos.2005.04.063 10.1016/j.physleta.2007.11.026 10.1108/09615531211208042 10.1016/j.chaos.2005.10.032 10.1016/0375-9601(96)00103-X 10.3844/ajassp.2015.836.846 10.1016/j.chaos.2005.04.071 10.1016/j.rinp.2015.07.001 10.1016/S0375-9601(96)00770-0 10.1016/j.mcm.2003.12.010 10.1016/j.physleta.2005.10.099 |
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Keywords | 65Z05 Riccati-Bernoulli Sub-ODE method 35A99 Phi-4 equation 35A20 Random variable Foam Drainage equation (stochastic) traveling wave solutions |
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References | Yan (b0095) 1996; 224 Khan (b0170) 2013; 23 El-Tawil MA, Sohaly MA. Mean square convergent finite difference scheme for random first order partial differential equations. The Egyptian Mathematical Society, International Conference on Mathematics, Trends and Development ICMTD12. Wazwaz (b0090) 2004; 40 Fan, Zhang (b0060) 2002; 305 Zhang, Wang, Wang, Fang (b0120) 2006; 350 Islam (b0190) 2015; 12 Malfliet, Hereman (b0040) 1996; 54 Wang, Zhang, Li (b0155) 2008; 372 He (b0145) 2004; 19 Ren, Zhang (b0115) 2006; 27 Wazwaz (b0135) 2007; 187 Wazwaz (b0045) 2004; 154 El-Tawil, Sohaly (b0015) 2011; 1 Wang (b0105) 1996; 213 Navarro-Quiles, Romero, Roselló, Sohaly (b0025) 2016; 2016 Helal, Mehanna (b0165) 2007; 190 Khan, Mohyud-Din (b0175) 2010; 11 Abdelrahman, Sohaly (b0005) 2017; 8 Alam (b0195) 2015; 5 Khan, Faraz, Yildirim (b0140) 2011; 24 Zhang, Tong, Wang (b0160) 2008; 372 Aminikhad, Moosaei, Hajipour (b0075) 2009; 26 Fan, Zhang (b0100) 1998; 246 Abdou (b0110) 2007; 31 Sayevand, Khan, Moradi, Fardi (b0150) 2015; 105 Ehsani, Hadi1, Hadi (b0180) 2013; 3 Akter, Akbar (b0185) 2015; 5 Fan (b0130) 2000; 277 Wazwaz (b0085) 2005; 50 Bekir, Uygun (b0205) 2012; 18 Abdelrahman, Zahran, Khater (b0065) 2015; 4 EL-Wakil, Abdou (b0125) 2007; 31 Sohaly (b0030) 2014; 2 Abdelrahman, Khater (b0050) 2015; 11 Mohyud-Din, Khan, Naeem, Yildirim (b0080) 2012; 22 Abdelrahman, Sohaly (b0010) 2017; 132 Dai, Zhang (b0055) 2006; 27 Yang, Deng, Wei (b0200) 2015; 1 He, Wu (b0070) 2006; 30 Malfliet (b0035) 1992; 60 Bekir (10.1016/j.rinp.2018.02.032_b0205) 2012; 18 Sayevand (10.1016/j.rinp.2018.02.032_b0150) 2015; 105 Malfliet (10.1016/j.rinp.2018.02.032_b0040) 1996; 54 Alam (10.1016/j.rinp.2018.02.032_b0195) 2015; 5 Aminikhad (10.1016/j.rinp.2018.02.032_b0075) 2009; 26 EL-Wakil (10.1016/j.rinp.2018.02.032_b0125) 2007; 31 Wazwaz (10.1016/j.rinp.2018.02.032_b0090) 2004; 40 Wang (10.1016/j.rinp.2018.02.032_b0105) 1996; 213 Helal (10.1016/j.rinp.2018.02.032_b0165) 2007; 190 Fan (10.1016/j.rinp.2018.02.032_b0130) 2000; 277 Sohaly (10.1016/j.rinp.2018.02.032_b0030) 2014; 2 Fan (10.1016/j.rinp.2018.02.032_b0060) 2002; 305 Wazwaz (10.1016/j.rinp.2018.02.032_b0045) 2004; 154 Mohyud-Din (10.1016/j.rinp.2018.02.032_b0080) 2012; 22 Zhang (10.1016/j.rinp.2018.02.032_b0160) 2008; 372 Fan (10.1016/j.rinp.2018.02.032_b0100) 1998; 246 Wang (10.1016/j.rinp.2018.02.032_b0155) 2008; 372 Khan (10.1016/j.rinp.2018.02.032_b0175) 2010; 11 El-Tawil (10.1016/j.rinp.2018.02.032_b0015) 2011; 1 Zhang (10.1016/j.rinp.2018.02.032_b0120) 2006; 350 Islam (10.1016/j.rinp.2018.02.032_b0190) 2015; 12 Khan (10.1016/j.rinp.2018.02.032_b0140) 2011; 24 10.1016/j.rinp.2018.02.032_b0020 Akter (10.1016/j.rinp.2018.02.032_b0185) 2015; 5 He (10.1016/j.rinp.2018.02.032_b0070) 2006; 30 Abdelrahman (10.1016/j.rinp.2018.02.032_b0005) 2017; 8 Abdelrahman (10.1016/j.rinp.2018.02.032_b0050) 2015; 11 Navarro-Quiles (10.1016/j.rinp.2018.02.032_b0025) 2016; 2016 Abdelrahman (10.1016/j.rinp.2018.02.032_b0065) 2015; 4 Wazwaz (10.1016/j.rinp.2018.02.032_b0135) 2007; 187 Abdelrahman (10.1016/j.rinp.2018.02.032_b0010) 2017; 132 Ren (10.1016/j.rinp.2018.02.032_b0115) 2006; 27 Khan (10.1016/j.rinp.2018.02.032_b0170) 2013; 23 Wazwaz (10.1016/j.rinp.2018.02.032_b0085) 2005; 50 Yan (10.1016/j.rinp.2018.02.032_b0095) 1996; 224 Dai (10.1016/j.rinp.2018.02.032_b0055) 2006; 27 He (10.1016/j.rinp.2018.02.032_b0145) 2004; 19 Ehsani (10.1016/j.rinp.2018.02.032_b0180) 2013; 3 Malfliet (10.1016/j.rinp.2018.02.032_b0035) 1992; 60 Abdou (10.1016/j.rinp.2018.02.032_b0110) 2007; 31 Yang (10.1016/j.rinp.2018.02.032_b0200) 2015; 1 |
References_xml | – volume: 27 start-page: 959 year: 2006 end-page: 979 ident: b0115 article-title: A generalized F-expansion method to find abundant families of Jacobi elliptic function solutions of the (2 + 1)-dimensional Nizhnik-Novikov-Veselov equation publication-title: Chaos, Solitons Fractals – volume: 372 start-page: 417 year: 2008 end-page: 423 ident: b0155 article-title: The publication-title: Phys Lett A – volume: 23 start-page: 411 year: 2013 end-page: 415 ident: b0170 article-title: A method for solving nonlinear time-dependent drainage model publication-title: Neural Comput Appl – volume: 224 start-page: 77 year: 1996 end-page: 84 ident: b0095 article-title: A simple transformation for nonlinear waves publication-title: Phys Lett A – volume: 11 start-page: 3134 year: 2015 end-page: 3138 ident: b0050 article-title: Traveling wave solutions for the couple Boiti-Leon-Pempinelli system by using extended Jacobian elliptic function expansion method publication-title: Adv Phys – volume: 132 start-page: 339 year: 2017 ident: b0010 article-title: Solitary waves for the nonlinear Schrödinger problem with the probability distribution function in stochastic input case publication-title: Eur Phys J Plus – volume: 31 start-page: 95 year: 2007 end-page: 104 ident: b0110 article-title: The extended F-expansion method and its application for a class of nonlinear evolution equations publication-title: Chaos, Solitons Fractals – volume: 11 start-page: 1103 year: 2010 end-page: 1107 ident: b0175 article-title: Coupling of He’s polynomials and Laplace transformation for MHD viscous flow over a stretching sheet publication-title: Int J Nonlinear Sci Numer Simul – volume: 1 start-page: 66 year: 2011 ident: b0015 article-title: Mean square numerical methods for initial value random differential equations publication-title: Open J Discrete Math – volume: 246 start-page: 403 year: 1998 end-page: 406 ident: b0100 article-title: A note on the homogeneous balance method publication-title: Phys Lett A – volume: 187 start-page: 1131 year: 2007 end-page: 1142 ident: b0135 article-title: The extended tanh method for abundant solitary wave solutions of nonlinear wave equations publication-title: Appl Math Comput – volume: 24 start-page: 965 year: 2011 end-page: 968 ident: b0140 article-title: New soliton solutions of the generalized Zakharov equations using He’s variational approach publication-title: Appl Math Lett – volume: 5 start-page: 125 year: 2015 end-page: 130 ident: b0185 article-title: Exact solutions to the Benney-Luke equation and the Phi-4 equations by using modified simple equation method publication-title: Results Phys – volume: 305 start-page: 383 year: 2002 end-page: 392 ident: b0060 article-title: Applications of the Jacobi elliptic function method to special-type nonlinear equations publication-title: Phys Lett A – volume: 190 start-page: 599 year: 2007 end-page: 609 ident: b0165 article-title: The tanh method and Adomian decomposition method for solving the foam drainage equation publication-title: Appl Math Comput – volume: 22 start-page: 335 year: 2012 end-page: 341 ident: b0080 article-title: Exp-function method for solitary and periodic solutions of Fitzhugh Nagumo equations publication-title: Int J Numer Methods Heat Fluid Flow – volume: 50 start-page: 1685 year: 2005 end-page: 1696 ident: b0085 article-title: Exact solutions to the double sinh-Gordon equation by the tanh method and a variable separated ODE, method publication-title: Comput Math Appl – volume: 60 start-page: 650 year: 1992 end-page: 654 ident: b0035 article-title: Solitary wave solutions of nonlinear wave equation publication-title: Am J Phys – volume: 18 start-page: 73 year: 2012 end-page: 85 ident: b0205 article-title: Exact traveling wave solutions of nonlinear evolution equations by using the publication-title: Arab J Math Sci – volume: 54 start-page: 563 year: 1996 end-page: 568 ident: b0040 article-title: The tanh method: exact solutions of nonlinear evolution and wave equations publication-title: Phys Scr – volume: 30 start-page: 700 year: 2006 end-page: 708 ident: b0070 article-title: Exp-function method for nonlinear wave equations publication-title: Chaos, Solitons Fractals – volume: 372 start-page: 2254 year: 2008 end-page: 2257 ident: b0160 article-title: A generalized publication-title: Phys Lett A – volume: 154 start-page: 714 year: 2004 end-page: 723 ident: b0045 article-title: The tanh method for travelling wave solutions of nonlinear equations publication-title: Appl Math Comput – volume: 31 start-page: 840 year: 2007 end-page: 852 ident: b0125 article-title: New exact travelling wave solutions using modified extented tanh-function method publication-title: Chaos, Solitons Fractals – volume: 2 start-page: 164 year: 2014 end-page: 171 ident: b0030 article-title: Mean square convergent three and five points finite difference scheme for stochastic parabolic partial differential equations publication-title: Electron J Math Anal Appl – volume: 27 start-page: 1042 year: 2006 end-page: 1049 ident: b0055 article-title: Jacobian elliptic function method for nonlinear differential difference equations publication-title: Chaos, Solitons Fractals – volume: 277 start-page: 212 year: 2000 end-page: 218 ident: b0130 article-title: Extended tanh-function method and its applications to nonlinear equations publication-title: Phys Lett A – volume: 19 start-page: 847 year: 2004 end-page: 851 ident: b0145 article-title: Variational principles for some nonlinear partial differential equations with variable coefficients publication-title: Chaos, Solitons Fractals – volume: 26 start-page: 1427 year: 2009 end-page: 1433 ident: b0075 article-title: Exact solutions for nonlinear partial differential equations via Exp-function method publication-title: Numer Methods Partial Differ Equ – volume: 2016 start-page: 7 year: 2016 ident: b0025 article-title: Approximating the solution stochastic process of the random Cauchy one-dimensional heat model publication-title: Abs Appl Anal – volume: 1 start-page: 117 year: 2015 end-page: 133 ident: b0200 article-title: A Riccati-Bernoulli sub-ODE method for nonlinear partial differential equations and its application publication-title: Adv Differ Equ – volume: 3 start-page: 1378 year: 2013 end-page: 1388 ident: b0180 article-title: Analytical solution of phi-four equation publication-title: Tech J Eng Appl Sci – volume: 350 start-page: 103 year: 2006 end-page: 109 ident: b0120 article-title: The improved F-expansion method and its applications publication-title: Phys Lett A – volume: 4 start-page: 37 year: 2015 end-page: 47 ident: b0065 article-title: The publication-title: Int J Mod Nonlinear Theory Appl – volume: 8 year: 2017 ident: b0005 article-title: Solitary waves for the modified Korteweg-De Vries equation in deterministic case and random case publication-title: J Phys Math – volume: 40 start-page: 499 year: 2004 end-page: 508 ident: b0090 article-title: A sine-cosine method for handling nonlinear wave equations publication-title: Math Comput Model – reference: El-Tawil MA, Sohaly MA. Mean square convergent finite difference scheme for random first order partial differential equations. The Egyptian Mathematical Society, International Conference on Mathematics, Trends and Development ICMTD12. – volume: 213 start-page: 279 year: 1996 end-page: 287 ident: b0105 article-title: Exct solutions for a compound KdV-Burgers equation publication-title: Phys Lett A – volume: 105 start-page: 361 year: 2015 end-page: 373 ident: b0150 article-title: Finding the generalized solitary wave solutions within the publication-title: Cmes-Comput Model Eng Sci – volume: 12 start-page: 836 year: 2015 end-page: 846 ident: b0190 article-title: Application of an enhanced publication-title: Am J Appl Sci – volume: 5 start-page: 168 year: 2015 end-page: 177 ident: b0195 article-title: Exact solutions to the foam drainage equation by using the new generalized publication-title: Results Phys – volume: 2 start-page: 164 issue: 1 year: 2014 ident: 10.1016/j.rinp.2018.02.032_b0030 article-title: Mean square convergent three and five points finite difference scheme for stochastic parabolic partial differential equations publication-title: Electron J Math Anal Appl – volume: 190 start-page: 599 year: 2007 ident: 10.1016/j.rinp.2018.02.032_b0165 article-title: The tanh method and Adomian decomposition method for solving the foam drainage equation publication-title: Appl Math Comput – volume: 23 start-page: 411 issue: 2 year: 2013 ident: 10.1016/j.rinp.2018.02.032_b0170 article-title: A method for solving nonlinear time-dependent drainage model publication-title: Neural Comput Appl doi: 10.1007/s00521-012-0933-2 – volume: 1 start-page: 117 year: 2015 ident: 10.1016/j.rinp.2018.02.032_b0200 article-title: A Riccati-Bernoulli sub-ODE method for nonlinear partial differential equations and its application publication-title: Adv Differ Equ doi: 10.1186/s13662-015-0452-4 – volume: 31 start-page: 95 year: 2007 ident: 10.1016/j.rinp.2018.02.032_b0110 article-title: The extended F-expansion method and its application for a class of nonlinear evolution equations publication-title: Chaos, Solitons Fractals doi: 10.1016/j.chaos.2005.09.030 – volume: 277 start-page: 212 year: 2000 ident: 10.1016/j.rinp.2018.02.032_b0130 article-title: Extended tanh-function method and its applications to nonlinear equations publication-title: Phys Lett A doi: 10.1016/S0375-9601(00)00725-8 – volume: 1 start-page: 66 issue: 02 year: 2011 ident: 10.1016/j.rinp.2018.02.032_b0015 article-title: Mean square numerical methods for initial value random differential equations publication-title: Open J Discrete Math doi: 10.4236/ojdm.2011.12009 – volume: 305 start-page: 383 year: 2002 ident: 10.1016/j.rinp.2018.02.032_b0060 article-title: Applications of the Jacobi elliptic function method to special-type nonlinear equations publication-title: Phys Lett A doi: 10.1016/S0375-9601(02)01516-5 – volume: 60 start-page: 650 year: 1992 ident: 10.1016/j.rinp.2018.02.032_b0035 article-title: Solitary wave solutions of nonlinear wave equation publication-title: Am J Phys doi: 10.1119/1.17120 – volume: 372 start-page: 417 year: 2008 ident: 10.1016/j.rinp.2018.02.032_b0155 article-title: The G′G-expansion method and travelling wave solutions of nonlinear evolutions equations in mathematical physics publication-title: Phys Lett A doi: 10.1016/j.physleta.2007.07.051 – volume: 105 start-page: 361 issue: 5 year: 2015 ident: 10.1016/j.rinp.2018.02.032_b0150 article-title: Finding the generalized solitary wave solutions within the G′G-expansion method publication-title: Cmes-Comput Model Eng Sci – volume: 11 start-page: 3134 issue: 3 year: 2015 ident: 10.1016/j.rinp.2018.02.032_b0050 article-title: Traveling wave solutions for the couple Boiti-Leon-Pempinelli system by using extended Jacobian elliptic function expansion method publication-title: Adv Phys doi: 10.24297/jap.v11i3.470 – volume: 4 start-page: 37 issue: 1 year: 2015 ident: 10.1016/j.rinp.2018.02.032_b0065 article-title: The Exp(-ϕ(ξ))-expansion method and its application for solving nonlinear evolution equations publication-title: Int J Mod Nonlinear Theory Appl doi: 10.4236/ijmnta.2015.41004 – volume: 26 start-page: 1427 year: 2009 ident: 10.1016/j.rinp.2018.02.032_b0075 article-title: Exact solutions for nonlinear partial differential equations via Exp-function method publication-title: Numer Methods Partial Differ Equ doi: 10.1002/num.20497 – volume: 246 start-page: 403 year: 1998 ident: 10.1016/j.rinp.2018.02.032_b0100 article-title: A note on the homogeneous balance method publication-title: Phys Lett A doi: 10.1016/S0375-9601(98)00547-7 – volume: 8 issue: 1 year: 2017 ident: 10.1016/j.rinp.2018.02.032_b0005 article-title: Solitary waves for the modified Korteweg-De Vries equation in deterministic case and random case publication-title: J Phys Math – volume: 54 start-page: 563 year: 1996 ident: 10.1016/j.rinp.2018.02.032_b0040 article-title: The tanh method: exact solutions of nonlinear evolution and wave equations publication-title: Phys Scr doi: 10.1088/0031-8949/54/6/003 – volume: 50 start-page: 1685 year: 2005 ident: 10.1016/j.rinp.2018.02.032_b0085 article-title: Exact solutions to the double sinh-Gordon equation by the tanh method and a variable separated ODE, method publication-title: Comput Math Appl doi: 10.1016/j.camwa.2005.05.010 – volume: 5 start-page: 125 year: 2015 ident: 10.1016/j.rinp.2018.02.032_b0185 article-title: Exact solutions to the Benney-Luke equation and the Phi-4 equations by using modified simple equation method publication-title: Results Phys doi: 10.1016/j.rinp.2015.01.008 – volume: 30 start-page: 700 year: 2006 ident: 10.1016/j.rinp.2018.02.032_b0070 article-title: Exp-function method for nonlinear wave equations publication-title: Chaos, Solitons Fractals doi: 10.1016/j.chaos.2006.03.020 – ident: 10.1016/j.rinp.2018.02.032_b0020 – volume: 19 start-page: 847 issue: 4 year: 2004 ident: 10.1016/j.rinp.2018.02.032_b0145 article-title: Variational principles for some nonlinear partial differential equations with variable coefficients publication-title: Chaos, Solitons Fractals doi: 10.1016/S0960-0779(03)00265-0 – volume: 18 start-page: 73 year: 2012 ident: 10.1016/j.rinp.2018.02.032_b0205 article-title: Exact traveling wave solutions of nonlinear evolution equations by using the G′G-expansion method publication-title: Arab J Math Sci doi: 10.1016/j.ajmsc.2011.08.002 – volume: 132 start-page: 339 year: 2017 ident: 10.1016/j.rinp.2018.02.032_b0010 article-title: Solitary waves for the nonlinear Schrödinger problem with the probability distribution function in stochastic input case publication-title: Eur Phys J Plus doi: 10.1140/epjp/i2017-11607-5 – volume: 24 start-page: 965 issue: 6 year: 2011 ident: 10.1016/j.rinp.2018.02.032_b0140 article-title: New soliton solutions of the generalized Zakharov equations using He’s variational approach publication-title: Appl Math Lett doi: 10.1016/j.aml.2011.01.006 – volume: 11 start-page: 1103 year: 2010 ident: 10.1016/j.rinp.2018.02.032_b0175 article-title: Coupling of He’s polynomials and Laplace transformation for MHD viscous flow over a stretching sheet publication-title: Int J Nonlinear Sci Numer Simul doi: 10.1515/IJNSNS.2010.11.12.1103 – volume: 27 start-page: 959 year: 2006 ident: 10.1016/j.rinp.2018.02.032_b0115 article-title: A generalized F-expansion method to find abundant families of Jacobi elliptic function solutions of the (2 + 1)-dimensional Nizhnik-Novikov-Veselov equation publication-title: Chaos, Solitons Fractals doi: 10.1016/j.chaos.2005.04.063 – volume: 2016 start-page: 7 year: 2016 ident: 10.1016/j.rinp.2018.02.032_b0025 article-title: Approximating the solution stochastic process of the random Cauchy one-dimensional heat model publication-title: Abs Appl Anal – volume: 372 start-page: 2254 year: 2008 ident: 10.1016/j.rinp.2018.02.032_b0160 article-title: A generalized G′G-expansion method for the mKdv equation with variable coefficients publication-title: Phys Lett A doi: 10.1016/j.physleta.2007.11.026 – volume: 154 start-page: 714 year: 2004 ident: 10.1016/j.rinp.2018.02.032_b0045 article-title: The tanh method for travelling wave solutions of nonlinear equations publication-title: Appl Math Comput – volume: 22 start-page: 335 year: 2012 ident: 10.1016/j.rinp.2018.02.032_b0080 article-title: Exp-function method for solitary and periodic solutions of Fitzhugh Nagumo equations publication-title: Int J Numer Methods Heat Fluid Flow doi: 10.1108/09615531211208042 – volume: 31 start-page: 840 year: 2007 ident: 10.1016/j.rinp.2018.02.032_b0125 article-title: New exact travelling wave solutions using modified extented tanh-function method publication-title: Chaos, Solitons Fractals doi: 10.1016/j.chaos.2005.10.032 – volume: 187 start-page: 1131 year: 2007 ident: 10.1016/j.rinp.2018.02.032_b0135 article-title: The extended tanh method for abundant solitary wave solutions of nonlinear wave equations publication-title: Appl Math Comput – volume: 213 start-page: 279 year: 1996 ident: 10.1016/j.rinp.2018.02.032_b0105 article-title: Exct solutions for a compound KdV-Burgers equation publication-title: Phys Lett A doi: 10.1016/0375-9601(96)00103-X – volume: 12 start-page: 836 year: 2015 ident: 10.1016/j.rinp.2018.02.032_b0190 article-title: Application of an enhanced G′G-expansion method to find exact solution of nonlinear PDEs in particle physics publication-title: Am J Appl Sci doi: 10.3844/ajassp.2015.836.846 – volume: 27 start-page: 1042 year: 2006 ident: 10.1016/j.rinp.2018.02.032_b0055 article-title: Jacobian elliptic function method for nonlinear differential difference equations publication-title: Chaos, Solitons Fractals doi: 10.1016/j.chaos.2005.04.071 – volume: 5 start-page: 168 year: 2015 ident: 10.1016/j.rinp.2018.02.032_b0195 article-title: Exact solutions to the foam drainage equation by using the new generalized G′G-expansion method publication-title: Results Phys doi: 10.1016/j.rinp.2015.07.001 – volume: 224 start-page: 77 year: 1996 ident: 10.1016/j.rinp.2018.02.032_b0095 article-title: A simple transformation for nonlinear waves publication-title: Phys Lett A doi: 10.1016/S0375-9601(96)00770-0 – volume: 3 start-page: 1378 year: 2013 ident: 10.1016/j.rinp.2018.02.032_b0180 article-title: Analytical solution of phi-four equation publication-title: Tech J Eng Appl Sci – volume: 40 start-page: 499 year: 2004 ident: 10.1016/j.rinp.2018.02.032_b0090 article-title: A sine-cosine method for handling nonlinear wave equations publication-title: Math Comput Model doi: 10.1016/j.mcm.2003.12.010 – volume: 350 start-page: 103 year: 2006 ident: 10.1016/j.rinp.2018.02.032_b0120 article-title: The improved F-expansion method and its applications publication-title: Phys Lett A doi: 10.1016/j.physleta.2005.10.099 |
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Snippet | In the present work, accuracy method called, Riccati-Bernoulli Sub-ODE technique is used for solving the deterministic and stochastic case of the Phi-4... |
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SubjectTerms | Foam Drainage equation (stochastic) traveling wave solutions Phi-4 equation Random variable Riccati-Bernoulli Sub-ODE method |
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Title | The development of the deterministic nonlinear PDEs in particle physics to stochastic case |
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