Exact travelling wave solutions for the generalized nonlinear Schrödinger (GNLS) equation with a source by extended tanh-coth, sine-cosine and exp-function methods

DOI10.1016/j.amc.2009.01.002zbMath1173.35690OpenAlexW2139253327MaRDI QIDQ1021534

J. Martínez

Publication date: 8 June 2009

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2009.01.002

zbMATH Keywords

generalized nonlinear Schrödinger equationexp-function methodsine-cosine methodextended tanh-coth method

Mathematics Subject Classification ID

Analyticity in context of PDEs (35A20) NLS equations (nonlinear Schrödinger equations) (35Q55) Solutions to PDEs in closed form (35C05)

Related Items (9)

Perturbation-induced chaos in nonlinear Schrödinger equation with single source and its characterization ⋮ Observations on the tanh-coth expansion method for finding solutions to nonlinear evolution equations ⋮ Exp‐function method for solitary and periodic solutions of Fitzhugh‐Nagumo equation ⋮ The first integral method to the nonlinear Schrödinger equations in higher dimensions ⋮ Generalized hyperbolic function solution to a class of nonlinear Schrödinger-type equations ⋮ Exact solutions for the nonlinear Schrödinger equation with variable coefficients using the generalized extended tanh-function, the sine-cosine and the exp-function methods ⋮ Elementary functions for constructing exact solutions to nonlinear partial differential equations with applications to nonlinear Schrödinger type and MHD equations ⋮ Generalization of exp-function and other standard function methods ⋮ Exact solutions of nonlinear Schrödinger equation by using symbolic computation

Cites Work

• Generalized solitary solution and compacton-like solution of the Jaulent-Miodek equations using the Exp-function method
• Exact solitary wave solutions for some nonlinear evolution equations via Exp-function method
• Application of Exp-function method to a KdV equation with variable coefficients
• Approximate explicit solutions of nonlinear BBMB equations by He's methods and comparison with the exact solution
• Solitary solutions, periodic solutions and compacton-like solutions using the Exp-function method
• A study on linear and nonlinear Schrödinger equations by the variational iteration method
• Exp-function method for nonlinear wave equations
• Solitary wave solutions of the generalized shallow water wave (GSWW) equation by Hirota's method, tanh-coth method and exp-function method
• Application of exp-function method to high-dimensional nonlinear evolution equation
• Solitary wave solutions for modified forms of Degasperis-Procesi and Camassa-Holm equations
• Exp-function based solution of nonlinear Radhakrishnan, Kundu and Laskshmanan (RKL) equation
• Solitary wave solutions for a generalized Hirota-Satsuma coupled KdV equation by homotopy perturbation method
• A coupling method of a homotopy technique and a perturbation technique for nonlinear problems
• Generalized extended tanh-function method and its application to \((1+1)\)-dimensional dispersive long wave equation
• The application of He's homotopy perturbation method to nonlinear equations arising in heat transfer
• The extended tanh method and its applications for solving nonlinear physical models
• The tanh method for travelling wave solutions to the Zhiber-Shabat equation and other related equations
• A note on the homogeneous balance method
• The \(\tan h\) method: solitons and periodic solutions for the Dodd-Bullough-Mikhailov and the Tzitzeica-Dodd-Bullough equations
• Application of homotopy perturbation method to nonlinear wave equations
• New periodic solutions for nonlinear evolution equations using Exp-function method
• New exact travelling wave solutions for the generalized nonlinear Schrödinger equation with a source
• The tanh and the sine-cosine methods for a reliable treatment of the modified equal width equation and its variants
• The tanh method: exact solutions of the sine-Gordon and the sinh-Gordon equations
• Extended tanh-function method and its applications to nonlinear equations
• Solitary wave solutions of nonlinear wave equations
• AN ELEMENTARY INTRODUCTION TO RECENTLY DEVELOPED ASYMPTOTIC METHODS AND NANOMECHANICS IN TEXTILE ENGINEERING
• The tanh method: II. Perturbation technique for conservative systems
• The tanh method and the sine–cosine method for solving the KP-MEW equation
• Envelope exact solutions for the generalized nonlinear Schrödinger equation with a source
• Variational iteration method for autonomous ordinary differential systems

This page was built for publication: Exact travelling wave solutions for the generalized nonlinear Schrödinger (GNLS) equation with a source by extended tanh-coth, sine-cosine and exp-function methods