Extended auxiliary equation method and its applications for finding the exact solutions for a class of nonlinear Schrödinger-type equations

DOI10.1016/j.amc.2016.04.014zbMath1410.35220OpenAlexW2400505019MaRDI QIDQ1733625

K. A. E. Alurrfi, Elsayed M. E. Zayed

Publication date: 21 March 2019

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

Full work available at URL: https://doi.org/10.1016/j.amc.2016.04.014

zbMATH Keywords

solitary wave solutionstrigonometric solutionsJacobi elliptic function solutionsextended auxiliary equation methodnonlinear PDEs in mathematical physics

Mathematics Subject Classification ID

Periodic solutions to PDEs (35B10) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton solutions (35C08)

Related Items (13)

New extended auxiliary equation method for finding many new Jacobi elliptic function solutions of three nonlinear Schrödinger equations ⋮ The solitary wave, kink and anti-kink solutions coexist at the same speed in a perturbed nonlinear Schrödinger equation ⋮ Optical solitons of model with integrable equation for wave packet envelope ⋮ Solitons and other exact solutions for two nonlinear PDEs in mathematical physics using the generalized projective Riccati equations method ⋮ Soliton solution of high‐order nonlinear Schrödinger equation based on ansatz method ⋮ Dynamics of optical solitons in the (2 + 1)-dimensional chiral nonlinear Schrödinger equation ⋮ Solitons and other solutions for higher-order NLS equation and quantum ZK equation using the extended simplest equation method ⋮ On solving the (3+1)-dimensional NLEQZK equation and the (3+1)-dimensional NLmZK equation using the extended simplest equation method ⋮ ON KINK AND ANTI-KINK WAVE SOLUTIONS OF SCHRÖDINGER EQUATION WITH DISTRIBUTED DELAY ⋮ Lie symmetry analysis and dynamic behaviors for nonlinear generalized Zakharov system ⋮ New Jacobi elliptic solutions and other solutions with quadratic-cubic nonlinearity using two mathematical methods ⋮ Unnamed Item ⋮ Bifurcation of traveling wave solutions for \((1+1)\)-dimensional resonant nonlinear Schrödinger equation

Uses Software

• ATFM

Cites Work

• Unnamed Item
• Unnamed Item
• Symbolic computation of some new nonlinear partial differential equations of nanobiosciences using modified extended tanh-function method
• The \(\left(\frac{G^\prime}{G}\right)\)-expansion method for the nonlinear lattice equations
• Generalized Jacobi elliptic function solution to a class of nonlinear Schrödinger-type equations
• The \((\frac{G'}{G})\)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics
• Exact travelling wave solutions for four forms of nonlinear Klein-Gordon equations
• Constructing of new exact solutions to the GKdV-mKdV equation with any-order nonlinear terms by \((\frac{G'}{G})\)-expansion method
• Using \(\left( \frac{G^{\prime}}{G} \right)\)-expansion method to seek the traveling wave solution of Kolmogorov-Petrovskii-Piskunov equation
• Exact solitary waves of the Fisher equation
• Application of Exp-function method for 2D cubic-quintic Ginzburg-Landau equation
• A new auxiliary equation and exact travelling wave solutions of nonlinear equations
• The (\(\frac{G'}{G})\)-expansion method and its applications to some nonlinear evolution equations in the mathematical physics
• An automated \(\tanh\)-function method for finding solitary wave solutions to nonlinear evolution equations
• The \((G'/ G, 1 / G)\)-expansion method and its applications to find the exact solutions of nonlinear PDEs for nanobiosciences
• The \((G' / G, 1 / G)\)-expansion method and its applications for solving two higher order nonlinear evolution equations
• The Jacobi elliptic equation method for solving fractional partial differential equations
• Extended auxiliary equation method and its applications to three generalized NLS equations
• The two-variable \((G'/G, 1/G)\)-expansion method for solving the nonlinear KdV-mKdV equation
• Travelling solitary wave solutions to a compound KdV-Burgers equation.
• On solving two higher-order nonlinear PDEs describing the propagation of optical pulses in optic fibers using the \((\frac{G^\prime}{G},\frac{1}{G})\)-expansion method
• Bäcklund transformation of fractional Riccati equation and its applications to nonlinear fractional partial differential equations
• Auxiliary equation method and new solutions of Klein-Gordon equations
• Simplest equation method to look for exact solutions of nonlinear differential equations
• Exact Solution of the Korteweg—de Vries Equation for Multiple Collisions of Solitons
• The Painlevé property for partial differential equations
• The tanh method: I. Exact solutions of nonlinear evolution and wave equations
• Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations

This page was built for publication: Extended auxiliary equation method and its applications for finding the exact solutions for a class of nonlinear Schrödinger-type equations