The first integral method to the nonlinear Schrödinger equations in higher dimensions
type: Item
instance of: scholarly article
title: The first integral method to the nonlinear Schrödinger equations in higher dimensions
zbMATH Open document ID: 1308.35048
DOI: 10.1155/2013/349173
author: S. I. El-Ganaini
published in: Abstract and Applied Analysis
publication date: 2013-05-08T00:00:00Z
review text: Summary: The first integral method introduced by \textit{Z. Feng} [J. Phys. A, Math. Gen. 35, No. 2, 343--349 (2002; Zbl 1040.35096)] is adopted for solving some important nonlinear partial differential equations, including the \((2 + 1)\)-dimensional hyperbolic nonlinear Schrödinger (HNLS) equation, the generalized nonlinear Schrödinger (GNLS) equation with a source, and the higher-order nonlinear Schrödinger equation in nonlinear optical fibers. This method provides polynomial first integrals for autonomous planar systems. Through the established first integrals, exact traveling wave solutions are formally derived in a concise manner.
Mathematics Subject Classification ID: 35C07
Mathematics Subject Classification ID: 35Q55
zbMATH DE Number: 6161325
Wikidata QID: Q58916004
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/349173
OpenAlex ID: W2087048578
cites work: Exact Solutions of (2+1)-Dimensional HNLS Equation
cites work: Solitary wave solutions of the generalized shallow water wave (GSWW) equation by Hirota's method, tanh-coth method and exp-function method
cites work: Generalized solitary solution and compacton-like solution of the Jaulent-Miodek equations using the Exp-function method
cites work: The tanh and the sine-cosine methods for a reliable treatment of the modified equal width equation and its variants
cites work: Solitary wave solutions for modified forms of Degasperis-Procesi and Camassa-Holm equations
cites work: Extended tanh-function method and its applications to nonlinear equations
cites work: The extended tanh method and its applications for solving nonlinear physical models
cites work: Link between solitary waves and projective Riccati equations
cites work: New exact solutions for the \((2 + 1)\)-dimensional generalized Broer-Kaup system
cites work: The first-integral method to study the Burgers–Korteweg–de Vries equation
cites work: The first integral method to the two-dimensional Burgers-Korteweg-de Vries equation
cites work: Traveling wave solutions to a reaction-diffusion equation
cites work: Traveling waves to a Burgers-Korteweg-de Vries-type equation with higher-order nonlinearities
cites work: The first integral method for solving some important nonlinear partial differential equations
cites work: The first integral method for modified Benjamin-Bona-Mahony equation
cites work: Exact and explicit solutions to nonlinear evolution equations using the division theorem
cites work: Travelling wave solutions to the generalized Pochhammer-Chree (PC) equations using the first integral method
cites work: Q4897792
cites work: Exact solutions of the equation of one-dimensional motion of a Pion Meson particle in an atom using two different approaches
cites work: Q4918988
cites work: Lie symmetry analysis of the quantum Zakharov equations
cites work: A GENERALIZED SUB-EQUATION EXPANSION METHOD AND ITS APPLICATION TO THE NONLINEAR SCHRÖDINGER EQUATION IN INHOMOGENEOUS OPTICAL FIBER MEDIA
cites work: Envelope exact solutions for the generalized nonlinear Schrödinger equation with a source
cites work: New exact travelling wave solutions for the generalized nonlinear Schrödinger equation with a source
cites work: Exact travelling wave solutions for the generalized nonlinear Schrödinger (GNLS) equation with a source by extended tanh-coth, sine-cosine and exp-function methods
cites work: Generalized method and its application in the higher-order nonlinear Schrödinger equation in nonlinear optical fibres.
cites work: An Inter-modulated Solitary Wave Solution for the Higher Order Nonlinear Schrödinger Equation
cites work: Exact solutions for the higher-order nonlinear Schrödinger equation in nonlinear optical fibres
Recommended article: Q5260691
Recommended article: Exact solutions of the nonlinear Schrödinger equation by the first integral method
Recommended article: The first integral method to nonlinear partial differential equations
Recommended article: Q4859151
Recommended article: The first integral method and its application for deriving the exact solutions of a higher-order dispersive cubic-quintic nonlinear Schrödinger equation
Recommended article: Q5400315
Recommended article: Schrödinger equations with nonlinearity of integral type
Recommended article: The first integral method to some complex nonlinear partial differential equations
Recommended article: Q5185410
Recommended article: The first integral method and new exact solutions to a nonlinear dispersive-dissipative equation
description: scientific article; zbMATH DE number 6161325