Soliton-like solutions to the generalized Burgers-Huxley equation with variable coefficients

2013 ◽  
Vol 3 (4) ◽  
Author(s):  
Houria Triki ◽  
Abdul-Majid Wazwaz
Keyword(s):  
Evolution Equations ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
Travelling Wave ◽  
Variable Coefficients ◽  
Nonlinear Evolution Equations ◽  
Time Dependent ◽  
Physical Parameters ◽  
Ansatz Method ◽  
Huxley Equation

AbstractIn this paper, we consider the generalized Burgers-Huxley equation with arbitrary power of nonlinearity and timedependent coefficients. We analyze the traveling wave problem and explicitly find new soliton-like solutions for this extended equation by using the ansatz of Zhao et al. [X. Zhao, D. Tang, L. Wang, Phys. Lett. A 346 (2005) 288–291]. We also employ the solitary wave ansatz method to derive the exact bright and dark soliton solutions for the considered evolution equation. The physical parameters in the soliton solutions are obtained as function of the time-dependent model coefficients. The conditions of existence of solitons are presented. As a result, rich exact travelling wave solutions, which contain new soliton-like solutions, bell-shaped solitons and kink-shaped solitons for the generalized Burgers-Huxley equation with time-dependent coefficients, are obtained. The methods employed here can also be used to solve a large class of nonlinear evolution equations with variable coefficients.

Bright and dark solitons for a generalized Korteweg-de Vries–modified Korteweg-de Vries equation with high-order nonlinear terms and time-dependent coefficients

2011 ◽  
Vol 89 (3) ◽  
pp. 253-259 ◽  
Author(s):  
Houria Triki ◽  
Abdul-Majid Wazwaz
Keyword(s):  
Soliton Solutions ◽  
Dark Soliton ◽  
Mkdv Equation ◽  
High Order ◽  
Time Dependent ◽  
Physical Parameters ◽  
Ansatz Method ◽  
Envelope Solitons ◽  
De Vries ◽  
Exact Soliton Solutions

We consider a generalized Korteweg-de Vries–modified Korteweg-de Vries (KdV–mKdV) equation with high-order nonlinear terms and time-dependent coefficients. Bright and dark soliton solutions are obtained by means of the solitary wave ansatz method. The physical parameters in the soliton solutions are obtained as functions of the varying model coefficients. Parametric conditions for the existence of envelope solitons are given. In view of the analysis, we see that the method used is an efficient way to construct exact soliton solutions for such a generalized version of the KdV–mKdV equation with time-dependent coefficients and high-order nonlinear terms.

Exact Soliton Solutions of the Variable Coefficient KdV Equation with Forced Term

2014 ◽  
Vol 548-549 ◽  
pp. 1196-1200
Author(s):  
Yong Mei Bao ◽  
Siqintana Bao
Keyword(s):  
Variable Coefficient ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Kdv Equation ◽  
Soliton Solutions ◽  
Nonlinear Ordinary Differential Equation ◽  
Variable Coefficients ◽  
Nonlinear Evolution Equations ◽  
Forced Term ◽  
Exact Soliton Solutions

In order to construct exact soliton solutions of nonlinear evolution equations with variable coefficients. By using a transformation, the variable coefficient KdV equation with forced Term is reduced to nonlinear ordinary differential equation (NLODE), after that, a number of exact solitons solutions of variable coefficient KdV equation with forced Term are obtained by using the equation shorted in NLODE. As it showed above, this kind of method can be applied in solving a large number of nonlinear evolution equations.

scholarly journals BRIGHT AND DARK SOLITON SOLUTIONS OF THE (2 + 1)-DIMENSIONAL EVOLUTION EQUATIONS

2014 ◽  
Vol 19 (1) ◽  
pp. 118-126 ◽  
Author(s):  
Ahmet Bekir ◽  
Adem C. Cevikel ◽  
Ozkan Guner ◽  
Sait San
Keyword(s):  
Solitary Wave ◽  
Nonlinear Equations ◽  
Evolution Equations ◽  
Boussinesq Equation ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
Bright Soliton ◽  
Physical Parameters ◽  
Kp Equation ◽  
Constant Coefficients

In this paper, we obtained the 1-soliton solutions of the (2+1)-dimensional Boussinesq equation and the Camassa–Holm–KP equation. By using a solitary wave ansatz in the form of sechp function, we obtain exact bright soliton solutions and another wave ansatz in the form of tanhp function we obtain exact dark soliton solutions for these equations. The physical parameters in the soliton solutions are obtained nonlinear equations with constant coefficients.

scholarly journals Bright and dark 1– soliton solutions to perturbed Schrodinger – hirota equation with power law nonlinearity via semi – inverse variation method and ansatz method

2017 ◽  
Vol 5 (2) ◽  
pp. 39 ◽  
Author(s):  
S. Subhaschandra Singh
Keyword(s):  
Exact Solutions ◽  
Power Law ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Nonlinear Evolution Equations ◽  
Variation Method ◽  
Science And Engineering ◽  
Ansatz Method ◽  
Hirota Equation

This paper studies perturbed Schrodinger Hirota equation with power law nonlinearity by obtaining its 1 – soliton solutions via He’s semi – inverse variation method and the Ansatz method and the results reveal that these methods are very effective ones for obtaining exact solutions to various types of nonlinear evolution equations appearing in the studies of science and engineering.

scholarly journals New traveling wave structures for two higher dimensional nonlinear evolution equations with time-dependent coefficients: Horseshoe-like solitons and multiwave interaction solutions

2021 ◽  
Author(s):  
Yuxin Qin ◽  
Yinping Liu ◽  
Guiqiong Xu
Keyword(s):  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Variable Coefficients ◽  
Nonlinear Evolution Equations ◽  
Time Dependent ◽  
Interaction Solutions ◽  
Multiwave Interaction ◽  
Higher Dimensional ◽  
Multiwave Solutions

Abstract In this paper, by introducing new traveling wave transformations in specific nonlinear forms, a variety of new multiwave interaction solutions for two higher dimensional nonlinear evolution equations with time-dependent coefficients are investigated. These new kinds of multiwave solutions can enrich solutions of nonlinear evolution equations with variable coefficients.

Abundant New Exact Solutions of the Coupled Potential KdV Equation and the Modified KdV-Type Equation

2001 ◽  
Vol 56 (12) ◽  
pp. 809-815
Author(s):  
Zhenya Yan
Keyword(s):  
Exact Solutions ◽  
Evolution Equations ◽  
Kdv Equation ◽  
Soliton Solutions ◽  
Type Equation ◽  
Travelling Wave ◽  
Nonlinear Evolution Equations ◽  
Rational Solutions ◽  
Soliton Theory ◽  
Kdv Type Equations

Abstract Exact solutions of nonlinear evolution equations (NLEEs)in soliton theory and their applications are studied. A powerful method is established to search for exact travelling wave solutions of NLEEs. We chose the coupled potential KdV equation and modified KdV-type equations presented by Foursov to illustrate the approach with the aid of Maple. As a result, eight families of exact solutions of the coupled potential KdV equation and nine families of exact solutions of the modified KdV-type equations are obtained, which contain new kink-like soliton solutions, kink­ shaped solitons, bell-shaped solitons, periodic solutions, rational solutions and singular solitons. The properties of the solutions are shown in figures.

Dark Solitons for a Generalized Korteweg-de Vries Equation with Time-Dependent Coefficients

2011 ◽  
Vol 66 (3-4) ◽  
pp. 199-204
Author(s):  
Houria Triki ◽  
Abdul-Majid Wazwaz
Keyword(s):  
Pulse Propagation ◽  
Kdv Equation ◽  
Critical Rayleigh Number ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
Time Dependent ◽  
Ansatz Method ◽  
Wave Dynamics ◽  
De Vries ◽  
Dependent Model

We consider the evolution of long shallow waves in a convecting fluid when the critical Rayleigh number slightly exceeds its critical value within the framework of a perturbed Korteweg-de Vries (KdV) equation. In order to study the wave dynamics of nonlinear pulse propagation in an inhomogeneous KdV media, a generalized form of the considered model with time-dependent coefficients is presented. By means of the solitary wave ansatz method, exact dark soliton solutions are derived under certain parametric conditions. The results show that the soliton parameters (amplitude, inverse width, and velocity) are influenced by the time variation of the dependent model coefficients. The existence of such a soliton solution is the result of the exact balance among nonlinearity, third-order and fourth-order nonlinear dispersions, diffusion, dissipation, and reaction.

Sign in / Sign up

Export Citation Format

Share Document