Applications of the extended tanh method for coupled nonlinear evolution equations

DOI10.1016/j.cnsns.2007.05.001zbMath1221.35322OpenAlexW1994844467MaRDI QIDQ718765

Ahmet Bekir

Publication date: 24 September 2011

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2007.05.001

zbMATH Keywords

extended tanh method\((2 + 1)\)-dimensional Konopelchenko-Dubrovsky equationcoupled Hirota-KdV equationDrinfeld-Sokolov equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Soliton equations (35Q51)

Related Items

New exact travelling wave solutions of nonlinear physical models ⋮ The extended tanh method for solving systems of nonlinear wave equations ⋮ Bifurcation analysis and solitary-like wave solutions for extended \((2+1)\)-dimensional Konopelchenko-Dubrovsky equations ⋮ Trigonometric and hyperbolic type solutions to a generalized Drinfel'd-Sokolov equation ⋮ Solitons for the (2+1)-dimensional Konopelchenko-Dubrovsky equations ⋮ The \((G'/G)\)-expansion method for abundant traveling wave solutions of Caudrey-Dodd-Gibbon equation ⋮ New exponential and complex traveling wave solutions to the Konopelchenko-Dubrovsky model ⋮ Explicit exact solutions of some nonlinear evolution equations with their geometric interpretations ⋮ Application of the \((\frac{G'}{G})\)-expansion method for nonlinear evolution equations ⋮ Traveling wave solutions \((u,\nu)\) to a generalized Drinfel'd-Sokolov system which satisfy \(u=a_1\nu^m+a_0\) ⋮ The extended hyperbolic function method for generalized forms of nonlinear heat conduction and Huxley equations ⋮ Bifurcations of the time-fractional generalized coupled Hirota-Satsuma KdV system ⋮ Exact solutions of some nonlinear systems of partial differential equations by using the first integral method ⋮ Solitonic solutions for homogeneous KdV systems by homotopy analysis method ⋮ Analytical solutions to a generalized Drinfel'd-Sokolov equation related to DSSH and KdV6 ⋮ Explicit exact solutions for the \((2+1)\)-dimensional Boiti-Leon-Pempinelli equation. ⋮ On nonlinear dynamics of interacting populations: coupled kink waves in a system of two populations ⋮ Seven common errors in finding exact solutions of nonlinear differential equations ⋮ Conservation laws for a complexly coupled KdV system, coupled Burgers system and Drinfeld-Sokolov-Wilson system via multiplier approach ⋮ The non-traveling wave solutions and novel fractal soliton for the \((2 + 1)\)-dimensional Broer-Kaup equations with variable coefficients ⋮ A new expansion and new families of exact traveling solutions to Hirota equation ⋮ Research on nonlinear waves of blood flow in arterial vessels ⋮ Explicit exact solutions for the (2 + 1)-dimensional Konopelchenko-Dubrovsky equation ⋮ Soliton and periodic solutions for time-dependent coefficient non-linear equation ⋮ Comparison Of (G′/G)-Methods for Finding Exact Solutions of the Drinfeld-Sokolov System ⋮ Weierstrass elliptic solutions to a Zakharov equation in plasmas with power law nonlinearity

Cites Work

• Unnamed Item
• The sine-cosine method for obtaining solutions with compact and noncompact structures
• Two reliable methods for solving variants of the KdV equation with compact and noncompact structures
• New solitary wave solutions to the modified forms of Degasperis-Procesi and Camassa-Holm equations
• The extended tanh method for new solitons solutions for many forms of the fifth-order KdV equations
• New kinks and solitons solutions to the \((2+1)\)-dimensional Konopelchenko-Dubrovsky equation
• A Bäcklund transformation and the inverse scattering transform method for the generalised Vakhnenko equation
• Abundant families of Jacobi elliptic function solutions of the \((2+1)\)-dimensional integrable Davey-Stewartson-type equation via a new method
• The tanh method, a simple transformation and exact analytical solutions for nonlinear reaction-diffusion equations
• A sine-cosine method for handling nonlinear wave equations
• New compactons, solitons and periodic solutions for nonlinear variants of the KdV and the KP equations
• The tanh method for traveling wave solutions of nonlinear equations
• A note on the homogeneous balance method
• New exact travelling wave solutions using modified extended tanh-function method
• The \(\tan h\) method: solitons and periodic solutions for the Dodd-Bullough-Mikhailov and the Tzitzeica-Dodd-Bullough equations
• Nonlinear variants of the BBM equation with compact and noncompact physical structures
• The tanh method: exact solutions of the sine-Gordon and the sinh-Gordon equations
• Exact and explicit travelling wave solutions for the nonlinear Drinfeld--Sokolov system
• The tanh method for generalized forms of nonlinear heat conduction and Burgers-Fisher equations
• Travelling wave solutions of generalized forms of Burgers, Burgers-KdV and Burgers-Huxley equations
• Extended tanh-function method and its applications to nonlinear equations
• Solitary wave solutions of nonlinear wave equations
• The tanh method: I. Exact solutions of nonlinear evolution and wave equations