The exact solutions of the stochastic Ginzburg–Landau equation
The main goal of this paper is to obtain the exact solutions of the stochastic real-valued Ginzburg–Landau equation, which is forced by multiplicative noise in the Itô sense. It is necessary to get the exact solutions of this equation because it occurs in numerous fields of physics, mathematics and...
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| Published in | Results in physics Vol. 23; p. 103988 |
|---|---|
| Main Authors | , , , , , |
| Format | Journal Article |
| Language | English |
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Elsevier B.V
01.04.2021
Elsevier |
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| Online Access | Get full text |
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| Abstract | The main goal of this paper is to obtain the exact solutions of the stochastic real-valued Ginzburg–Landau equation, which is forced by multiplicative noise in the Itô sense. It is necessary to get the exact solutions of this equation because it occurs in numerous fields of physics, mathematics and chemistry. We use three different methods such as the tanh-coth, the Riccati-Bernoulli sub-ODE and the generalized G′G-expansion methods in order to obtain a new trigonometric and hyperbolic stochastic solutions. The main advantage of these three methods is their applicability in solving similar models. The novelty of the present paper is that the results obtained here extend and improve some results that were previously obtained. Moreover, we plot 3D surfaces of analytical solutions obtained in this paper by using Matlab to illustrate the impact of multiplicative noise on the solutions of the stochastic real-valued Ginzburg–Landau equation. |
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| AbstractList | The main goal of this paper is to obtain the exact solutions of the stochastic real-valued Ginzburg–Landau equation, which is forced by multiplicative noise in the Itô sense. It is necessary to get the exact solutions of this equation because it occurs in numerous fields of physics, mathematics and chemistry. We use three different methods such as the tanh-coth, the Riccati-Bernoulli sub-ODE and the generalized G′G-expansion methods in order to obtain a new trigonometric and hyperbolic stochastic solutions. The main advantage of these three methods is their applicability in solving similar models. The novelty of the present paper is that the results obtained here extend and improve some results that were previously obtained. Moreover, we plot 3D surfaces of analytical solutions obtained in this paper by using Matlab to illustrate the impact of multiplicative noise on the solutions of the stochastic real-valued Ginzburg–Landau equation. |
| ArticleNumber | 103988 |
| Author | Mohammed, Wael W. El-Morshedy, M. Ahmad, Hijaz ALy, E.S. Elabbasy, E.M. Hamza, Amjad E. |
| Author_xml | – sequence: 1 givenname: Wael W. surname: Mohammed fullname: Mohammed, Wael W. email: wael.mohammed@mans.edu.eg organization: Department of Mathematics, Faculty of Science, University of Ha’il, Ha’il 2440, Saudi Arabia – sequence: 2 givenname: Hijaz surname: Ahmad fullname: Ahmad, Hijaz email: hijaz555@gmail.com organization: Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy – sequence: 3 givenname: Amjad E. surname: Hamza fullname: Hamza, Amjad E. organization: Department of Mathematics, Faculty of Science, University of Ha’il, Ha’il 2440, Saudi Arabia – sequence: 4 givenname: E.S. surname: ALy fullname: ALy, E.S. email: elkhateeb@jazanu.edu.sa organization: Department of Mathematics, Faculty of science, Jazan University, P.O Box 218, Jazan, Saudi Arabia – sequence: 5 givenname: M. surname: El-Morshedy fullname: El-Morshedy, M. organization: Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia – sequence: 6 givenname: E.M. surname: Elabbasy fullname: Elabbasy, E.M. organization: Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt |
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| Keywords | Riccati-Bernoulli sub-ODE method G′G-expansion method 83C15 60H10 solitary wave solutions 35A20 tanh-coth method multiplicative noise 35Q51 60H15 Stochastic Ginzburg-Landau equation |
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| SubjectTerms | 35A20 35Q51 60H10 60H15 83C15 [formula omitted]-expansion method multiplicative noise Riccati-Bernoulli sub-ODE method solitary wave solutions Stochastic Ginzburg-Landau equation tanh-coth method |
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| Title | The exact solutions of the stochastic Ginzburg–Landau equation |
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