The first integral method and its application for deriving the exact solutions of a higher-order dispersive cubic-quintic nonlinear Schrödinger equation

DOI10.1007/s10598-015-9305-yzbMath1332.35344OpenAlexW2235233235MaRDI QIDQ259302

Yasser A. Amer, Elsayed M. E. Zayed

Publication date: 11 March 2016

Published in: Computational Mathematics and Modeling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10598-015-9305-y

zbMATH Keywords

exact solutionsfirst integral methoddivision theoremhigher-order dispersive cubic-quintic nonlinear Schrödinger equation

Mathematics Subject Classification ID

Wave equation (35L05) NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items

New extended auxiliary equation method for finding many new Jacobi elliptic function solutions of three nonlinear Schrödinger equations ⋮ New optical dromion and domain wall solutions of cascaded system in \((2+1)\)-dimensions via various analytical architectures ⋮ Bilinear equation of the nonlinear partial differential equation and its application ⋮ Exact combined solutions for the \((2+1)\)-dimensional dispersive long water-wave equations ⋮ Lie symmetry analysis and dynamic behaviors for nonlinear generalized Zakharov system ⋮ The exact solutions of generalized Davey-Stewartson equations with arbitrary power nonlinearities using the dynamical system and the first integral methods

Uses Software

• ATFM

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The \((\frac{G'}{G})\)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics
• Sub-ODE method and solitary wave solutions for higher order nonlinear Schrödinger equation
• Exact travelling wave solutions for four forms of nonlinear Klein-Gordon equations
• Exact solutions of the nonlinear Schrödinger equation by the first integral method
• A generalized \((\frac{G'}{G})\)-expansion method for the mKdV equation with variable coefficients
• Exact solutions for the nonlinear Schrödinger equation with variable coefficients using the generalized extended tanh-function, the sine-cosine and the exp-function methods
• The modified extended Fan sub-equation method and its application to the \((2+1)\)-dimensional Broer-Kaup-Kupershmidt equation
• Extended \(F\)-expansion method and periodic wave solutions for the generalized Zakharov equations
• Exp-function method for nonlinear wave equations
• The subsidiary ordinary differential equations and the exact solutions of the higher order dispersive nonlinear Schrödinger equation
• Travelling wave solutions of nonlinear partial equations by using the first integral method
• A new auxiliary equation and exact travelling wave solutions of nonlinear equations
• Some applications of the \((\frac{G'}{G})\)-expansion method to non-linear partial differential 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 periodic wave solutions for the Klein-Gordon-Schrödinger equations
• Abundant families of Jacobi elliptic function solutions of the \((2+1)\)-dimensional integrable Davey-Stewartson-type equation via a new method
• Solitary wave solutions for variant Boussinesq equations
• Modulational instability of nonlinear waves in the range of zero dispersion
• Exact solutions for a compound KdV-Burgers equation
• The periodic wave solutions and solitary wave solutions for a class of nonlinear partial differential equations
• A sub-ODE method for finding exact solutions of a generalized KdV-mKdV equation with high-order nonlinear terms
• Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics
• Various exact solutions of nonlinear Schrödinger equation with two nonlinear terms
• Auxiliary equation method and new solutions of Klein-Gordon equations
• Applications of F-expansion to periodic wave solutions for a new Hamiltonian amplitude equa\-tion
• Exact solutions for the high-order dispersive cubic-quintic nonlinear Schrödinger equation by the extended hyperbolic auxiliary equation method
• Explicit and exact solutions to a Kolmogorov-Petrovskii-Piskunov equation
• Extended tanh-function method and its applications to nonlinear equations
• Extended F -Expansion Method and Periodic Wave Solutions for Klein–Gordon–Schrödinger Equations
• New traveling wave solutions for higher dimensional nonlinear evolution equations using a generalized \big(\frac{G^{\prime}}{G}\big) -expansion method
• The first-integral method to study the Burgers–Korteweg–de Vries equation
• Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations
• New explicit travelling wave solutions for two new integrable coupled nonlinear evolution equations