New types of exact solutions for nonlinear Schrödinger equation with cubic nonlinearity

DOI10.1016/j.cam.2010.09.024zbMath1210.35231OpenAlexW2068759959MaRDI QIDQ629439

S. M. Khaled, Abd Elhalim Ebaid

Publication date: 9 March 2011

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

Full work available at URL: https://doi.org/10.1016/j.cam.2010.09.024

zbMATH Keywords

Schrödinger equationnonlinear equationsimproved F-expansion methodJacobi-elliptic functionsWeierstrass-elliptic function

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Solutions to PDEs in closed form (35C05) Methods of ordinary differential equations applied to PDEs (35A24) Trigonometric solutions to PDEs (35C09)

Related Items (11)

Superconvergence analysis of a new linearized MFEM for nonlinear Schrödinger equation ⋮ New exact solutions to the high dispersive cubic-quintic nonlinear Schrödinger equation ⋮ Unconditional convergence and optimal error estimates of the Euler semi-implicit scheme for a generalized nonlinear Schrödinger equation ⋮ Galerkin finite element method for damped nonlinear Schrödinger equation ⋮ Lie group analysis and propagation of weak discontinuity in one-dimensional ideal isentropic magnetogasdynamics ⋮ Nonconforming finite element method for a generalized nonlinear Schrödinger equation ⋮ New Exact Traveling Wave Solutions of the Unstable Nonlinear Schrödinger Equations ⋮ Exact solutions for the transformed reduced Ostrovsky equation via the \(F\)-expansion method in terms of Weierstrass-elliptic and Jacobian-elliptic functions ⋮ Comment on ``New types of exact solutions for nonlinear Schrödinger equation with cubic nonlinearity ⋮ Unconditionally optimal error estimates of a new mixed FEM for nonlinear Schrödinger equations ⋮ On integrability of nonautonomous nonlinear Schrödinger equations

Uses Software

• ATFM

Cites Work

• Unnamed Item
• Exact solitary wave solutions for some nonlinear evolution equations via Exp-function method
• A reliable treatment for nonlinear Schrödinger equations
• Generalized extended tanh-function method and its application
• Improved Jacobi-function method with symbolic computation to construct new double-periodic solutions for the generalized Ito system
• Extended Jacobi elliptic function expansion method and its applications
• New applications of developed Jacobi elliptic function expansion methods
• Exp-function method for nonlinear wave equations
• Exact solutions for the generalized Klein-Gordon equation via a transformation and exp-function method and comparison with Adomian's method
• Exact Jacobian elliptic function solutions and hyperbolic function solutions for Sawada-Kotere equation with variable coefficient
• An automated \(\tanh\)-function method for finding solitary wave solutions to nonlinear evolution equations
• On an improved complex tanh-function method
• New double periodic and multiple soliton solutions of the generalized \((2 + 1)\)-dimensional Boussinesq equation
• A note on the elliptic equation method
• Doubly periodic solutions of the modified Kawahara equation
• Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations
• New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations

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