New types of exact solutions for the fourth-order dispersive cubic–quintic nonlinear Schrödinger equation
In this study, we use two direct algebraic methods to solve a fourth-order dispersive cubic–quintic nonlinear Schrödinger equation, which is used to describe the propagation of optical pulse in a medium exhibiting a parabolic nonlinearity law. By using complex envelope ansatz method, we first obtain...
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| Published in | Applied mathematics and computation Vol. 217; no. 12; pp. 5967 - 5971 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Amsterdam
Elsevier Inc
15.02.2011
Elsevier |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0096-3003 1873-5649 |
| DOI | 10.1016/j.amc.2010.12.008 |
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| Abstract | In this study, we use two direct algebraic methods to solve a fourth-order dispersive cubic–quintic nonlinear Schrödinger equation, which is used to describe the propagation of optical pulse in a medium exhibiting a parabolic nonlinearity law. By using complex envelope ansatz method, we first obtain a new dark soliton and bright soliton, which may approach nonzero when the time variable approaches infinity. Then a series of analytical exact solutions are constructed by means of F-expansion method. These solutions include solitary wave solutions of the bell shape, solitary wave solutions of the kink shape, and periodic wave solutions of Jacobian elliptic function. |
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| AbstractList | In this study, we use two direct algebraic methods to solve a fourth-order dispersive cubic–quintic nonlinear Schrödinger equation, which is used to describe the propagation of optical pulse in a medium exhibiting a parabolic nonlinearity law. By using complex envelope ansatz method, we first obtain a new dark soliton and bright soliton, which may approach nonzero when the time variable approaches infinity. Then a series of analytical exact solutions are constructed by means of F-expansion method. These solutions include solitary wave solutions of the bell shape, solitary wave solutions of the kink shape, and periodic wave solutions of Jacobian elliptic function. |
| Author | Xu, Gui-Qiong |
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| Cites_doi | 10.1016/0030-4018(95)00552-8 10.1016/j.optlastec.2007.10.002 10.1103/PhysRevE.74.027602 10.1016/j.amc.2005.02.055 10.1016/j.chaos.2006.03.014 10.1002/sapm1967461133 10.1016/S0030-4018(02)02309-X 10.1103/PhysRevLett.84.4096 10.1103/PhysRevLett.78.448 10.1103/PhysRevLett.76.3955 10.1103/PhysRevE.60.3314 10.1103/PhysRevE.54.4312 10.1016/S0375-9601(02)01775-9 10.1016/j.physleta.2003.07.026 10.1016/j.chaos.2005.04.007 10.1016/j.amc.2009.09.024 10.1016/j.mcm.2005.08.010 10.1088/0305-4470/36/16/308 10.1016/j.cpc.2009.01.019 10.1016/j.physleta.2005.03.066 10.1103/PhysRevE.62.8719 10.1016/S0030-4018(97)00230-7 10.1016/j.physleta.2008.07.052 10.1016/j.amc.2008.12.004 |
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| Keywords | Soliton solution The nonlinear Schrödinger equation Periodic wave solution Numerical linear algebra Periodic solution Schrödinger equation Exact solution Non linear equation Direct method Numerical analysis Linear system Matrix inversion Applied mathematics Algebraic method Nonlinearity Analytical solution |
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| SubjectTerms | Exact sciences and technology Global analysis, analysis on manifolds Mathematical analysis Mathematics Numerical analysis Numerical analysis. Scientific computation Numerical linear algebra Partial differential equations Periodic wave solution Sciences and techniques of general use Soliton solution Special functions The nonlinear Schrödinger equation Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds |
| Title | New types of exact solutions for the fourth-order dispersive cubic–quintic nonlinear Schrödinger equation |
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