scholarly journals Bifurcation Analysis and Single Traveling Wave Solutions of the Variable-Coefficient Davey–Stewartson System

2022 ◽  
Vol 2022 ◽  
pp. 1-6
Author(s):  
Tianyong Han ◽  
Jiajin Wen ◽  
Zhao Li
Keyword(s):  
Traveling Wave ◽  
Variable Coefficient ◽  
Bifurcation Theory ◽  
Traveling Wave Solutions ◽  
Traveling Wave Solution ◽  
Wave Transformation ◽  
Wave Solutions ◽  
The One ◽  
Planar Dynamical Systems ◽  
Exact Traveling Wave Solution

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.

EXACT TRAVELING-WAVE SOLUTIONS FOR ONE-DIMENSIONAL MODIFIED KORTEWEG–DE VRIES EQUATION DEFINED ON CANTOR SETS

Fractals ◽  
2019 ◽  
Vol 27 (01) ◽  
pp. 1940010 ◽  
Author(s):  
FENG GAO ◽  
XIAO-JUN YANG ◽  
YANG JU
Keyword(s):  
Traveling Wave ◽  
Vries Equation ◽  
Traveling Wave Solutions ◽  
Mathematical Physics ◽  
Cantor Sets ◽  
Wave Transformation ◽  
One Dimensional ◽  
Wave Solutions ◽  
De Vries ◽  
The One

The one-dimensional modified Korteweg–de Vries equation defined on a Cantor set involving the local fractional derivative is investigated in this paper. With the aid of the fractal traveling-wave transformation technology, the nondifferentiable traveling-wave solutions for the problem are discussed in detail. The obtained results are accurate and efficient for describing the fractal water wave in mathematical physics.

Traveling wave solutions of the one-dimensional Boussinesq paradigm equation

2013 ◽  
Author(s):  
V. M. Vassilev ◽  
P. A. Djondjorov ◽  
M. Ts. Hadzhilazova ◽  
I. M. Mladenov
Keyword(s):  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
One Dimensional ◽  
Wave Solutions ◽  
The One

scholarly journals Single peaked traveling wave solutions to a generalized μ-Novikov Equation

2020 ◽  
Vol 10 (1) ◽  
pp. 66-75
Author(s):  
Byungsoo Moon
Keyword(s):  
Linear Combination ◽  
Traveling Wave ◽  
Wave Solution ◽  
Traveling Wave Solutions ◽  
Traveling Wave Solution ◽  
Wave Solutions ◽  
Quadratic Nonlinearities ◽  
Novikov Equation

Abstract In this paper, we study the existence of peaked traveling wave solution of the generalized μ-Novikov equation with nonlocal cubic and quadratic nonlinearities. The equation is a μ-version of a linear combination of the Novikov equation and Camassa-Hom equation. It is found that the equation admits single peaked traveling wave solutions.

Energy-carrying wave simulation of the Lonngren-wave equation in semiconductor materials

2021 ◽  
pp. 2150213
Author(s):  
Hülya Durur
Keyword(s):  
Wave Equation ◽  
Traveling Wave ◽  
Energy Transport ◽  
Three Dimensional ◽  
Traveling Wave Solutions ◽  
Traveling Wave Solution ◽  
Discussion Section ◽  
Advantages And Disadvantages ◽  
Wave Solutions ◽  
Package Program

In this study, the Lonngren-wave equation, which is physically semiconductor, is taken into consideration. Traveling wave solutions of this equation are presented with generalized exponential rational function method, which is one of the mathematically powerful analytical methods. These solutions are produced in bright (non-topological) soliton and complex trigonometric-type traveling wave solutions. Three-dimensional (3D), 2D and contour graphics are presented with the help of a ready-made package program with special values given to constants in these solutions. The effect of the change in wave velocity on the traveling wave solution showing energy transport is presented with the help of simulation. It is argued that velocity is one of the important factors in wave diffraction. In the results and discussion section, the advantages and disadvantages of the method are discussed.

Comparison exact and numerical simulation of the traveling wave solution in nonlinear dynamics

2020 ◽  
Vol 34 (29) ◽  
pp. 2050282
Author(s):  
Asıf Yokuş ◽  
Doğan Kaya
Keyword(s):  
Traveling Wave ◽  
Numerical Solutions ◽  
Traveling Wave Solutions ◽  
Transformation Method ◽  
Mkdv Equation ◽  
Traveling Wave Solution ◽  
Von Neumann ◽  
Wave Solutions ◽  
De Vries ◽  
The Stability

The traveling wave solutions of the combined Korteweg de Vries-modified Korteweg de Vries (cKdV-mKdV) equation and a complexly coupled KdV (CcKdV) equation are obtained by using the auto-Bäcklund Transformation Method (aBTM). To numerically approximate the exact solutions, the Finite Difference Method (FDM) is used. In addition, these exact traveling wave solutions and numerical solutions are compared by illustrating the tables and figures. Via the Fourier–von Neumann stability analysis, the stability of the FDM with the cKdV–mKdV equation is analyzed. The [Formula: see text] and [Formula: see text] norm errors are given for the numerical solutions. The 2D and 3D figures of the obtained solutions to these equations are plotted.

scholarly journals Approximate Damped Oscillatory Solutions for Generalized KdV-Burgers Equation and Their Error Estimates

2011 ◽  
Vol 2011 ◽  
pp. 1-26 ◽  
Author(s):  
Weiguo Zhang ◽  
Xiang Li
Keyword(s):  
Dynamical Systems ◽  
Error Estimates ◽  
Traveling Wave ◽  
Wave Solution ◽  
Burgers Equation ◽  
Traveling Wave Solutions ◽  
Approximate Solutions ◽  
Traveling Wave Solution ◽  
Oscillatory Solutions ◽  
Wave Solutions

We focus on studying approximate solutions of damped oscillatory solutions of generalized KdV-Burgers equation and their error estimates. The theory of planar dynamical systems is employed to make qualitative analysis to the dynamical systems which traveling wave solutions of this equation correspond to. We investigate the relations between the behaviors of bounded traveling wave solutions and dissipation coefficient, and give two critical valuesλ1andλ2which can characterize the scale of dissipation effect, for right and left-traveling wave solution, respectively. We obtain that for the right-traveling wave solution if dissipation coefficientα≥λ1, it appears as a monotone kink profile solitary wave solution; that if0<α<λ1, it appears as a damped oscillatory solution. This is similar for the left-traveling wave solution. According to the evolution relations of orbits in the global phase portraits which the damped oscillatory solutions correspond to, we obtain their approximate damped oscillatory solutions by undetermined coefficients method. By the idea of homogenization principle, we give the error estimates for these approximate solutions by establishing the integral equations reflecting the relations between exact and approximate solutions. The errors are infinitesimal decreasing in the exponential form.

scholarly journals New Exact Traveling Wave Solutions of the Time Fractional Complex Ginzburg-Landau Equation via the Conformable Fractional Derivative

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Zhao Li ◽  
Tianyong Han
Keyword(s):  
Traveling Wave ◽  
Landau Equation ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Wave Transformation ◽  
Hyperbolic Function ◽  
Ginzburg Landau ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
Ginzburg Landau Equation

In this study, the exact traveling wave solutions of the time fractional complex Ginzburg-Landau equation with the Kerr law and dual-power law nonlinearity are studied. The nonlinear fractional partial differential equations are converted to a nonlinear ordinary differential equation via a traveling wave transformation in the sense of conformable fractional derivatives. A range of solutions, which include hyperbolic function solutions, trigonometric function solutions, and rational function solutions, is derived by utilizing the new extended G ′ / G -expansion method. By selecting appropriate parameters of the solutions, numerical simulations are presented to explain further the propagation of optical pulses in optic fibers.

scholarly journals Traveling Wave Solutions and Chaotic Motions for a Perturbed Nonlinear Schrödinger Equation with Power-Law Nonlinearity and Higher-Order Dispersions

2021 ◽  
Author(s):  
Mati Youssoufa ◽  
Ousmanou Dafounansou ◽  
Camus Gaston Latchio Tiofack ◽  
Alidou Mohamadou
Keyword(s):  
Power Law ◽  
Traveling Wave ◽  
Bifurcation Theory ◽  
Chaotic Behavior ◽  
Traveling Wave Solutions ◽  
Chaotic Motions ◽  
Auxiliary Equation Method ◽  
Nonlinear Schrödinger ◽  
Wave Solutions ◽  
Quasiperiodic Route To Chaos

This chapter aims to study and solve the perturbed nonlinear Schrödinger (NLS) equation with the power-law nonlinearity in a nano-optical fiber, based upon different methods such as the auxiliary equation method, the Stuart and DiPrima’s stability analysis method, and the bifurcation theory. The existence of the traveling wave solutions is discussed, and their stability properties are investigated through the modulational stability gain spectra. Moreover, the development of the chaotic motions for the systems is pointed out via the bifurcation theory. Taking into account an external periodic perturbation, we have analyzed the chaotic behavior of traveling waves through quasiperiodic route to chaos.

Multiple wave solutions for nonlinear burgers equations using the multiple exp-function method

2021 ◽  
pp. 2150149
Author(s):  
Khaled A. Gepreel ◽  
E. M. E. Zayed
Keyword(s):  
Traveling Wave ◽  
Software Package ◽  
Function Method ◽  
Nonlinear Partial Differential Equations ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Mathematical Physics ◽  
Multiple Wave ◽  
Wave Solutions ◽  
The One

In this paper, we use the multiple exp-function method to explicity present traveling wave solutions, double-traveling wave (DTW) solutions and triple-traveling wave solutions (TWs) which include one-soliton, double-soliton and triple-soliton solutions for nonlinear partial differential equations (NPDEs) via, the (2+1)-dimensional and (3+1)-dimensional nonlinear Burgers PDEs in mathematical physics. In this work, we build some series of straightforward and new solutions successfully with the help of a computerized symbol computational software package like Maple or Mathematica. We will make some drawings in some cases with specific values for the relevant parameters for each obtained solutions such as the one-traveling wave solutions, double-traveling wave solutions and TWs. This method is efficient and powerful in solving a wide class of NPDEs.

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