New exact solutions for a generalized KdV equation

Discrete Dynamics in Nature and Society

Wen

2022

This paper mainly studies the bifurcation and single traveling wave solutions of the variable-coefficient Davey–Stewartson system. By employing the traveling wave transformation, the variable-coefficient Davey–Stewartson system is reduced to two-dimensional nonlinear ordinary differential equations. On the one hand, we use the bifurcation theory of planar dynamical systems to draw the phase diagram of the variable-coefficient Davey–Stewartson system. On the other hand, we use the polynomial complete discriminant method to obtain the exact traveling wave solution of the variable-coefficient Davey–Stewartson system.

Section: Traveling Wave Solutions Of System (1)mentioning

confidence: 99%

Bifurcation Analysis and Single Traveling Wave Solutions of the Variable‐Coefficient Davey–Stewartson System

Discrete Dynamics in Nature and Society

Wen

2022

“…where ξ 0 is the integration constant. e readers can refer to [2,4,18] for details of this method. e structure of this paper is as follows.…”

Section: α T U and D αmentioning

confidence: 99%

Classification of All Single Traveling Wave Solutions of Fractional Perturbed Gerdjikov–Ivanov Equation

Mathematical Problems in Engineering

2021

The fractional perturbed Gerdjikov–Ivanov (pGI) equation plays a momentous role in nonlinear fiber optics, especially in the application of photonic crystal fibers. Constructing traveling wave solutions to this equation is a very challenging task in physics and mathematics. In the current article, our main purpose is to give the classifications of traveling wave solutions of the fractional pGI equation. These results can help physicists to further explain the complex fractional pGI equation.

“…Let GðφÞ = φ 4 + a 2 φ 2 + a 1 φ + a 0 . Thus, we can obtain its complete discrimination system [21][22][23] as follows:…”

Section: The Classification Of Single Traveling Wave Solutions Via Complete Discrimination Systemsmentioning

confidence: 99%

Dynamical Behavior and the Classification of Single Traveling Wave Solutions for the Coupled Nonlinear Schrödinger Equations with Variable Coefficients

Zhao

Advances in Mathematical Physics

2021

In this paper, the dynamical properties and the classification of single traveling wave solutions of the coupled nonlinear Schrödinger equations with variable coefficients are investigated by utilizing the bifurcation theory and the complete discrimination system method. Firstly, coupled nonlinear Schrödinger equations with variable coefficients are transformed into coupled nonlinear ordinary differential equations by the traveling wave transformations. Then, phase portraits of coupled nonlinear Schrödinger equations with variable coefficients are plotted by selecting the suitable parameters. Furthermore, the traveling wave solutions of coupled nonlinear Schrödinger equations with variable coefficients which correspond to phase orbits are easily obtained by applying the method of planar dynamical systems, which can help us to further understand the propagation of the coupled nonlinear Schrödinger equations with variable coefficients in nonlinear optics. Finally, the periodic wave solutions, implicit analytical solutions, hyperbolic function solutions, and Jacobian elliptic function solutions of the coupled nonlinear Schrödinger equations with variable coefficients are constructed.