Painlevé integrability and new exact solutions of the \((4 + 1)\)-dimensional Fokas equation
type: Item
instance of: scholarly article
title: Painlevé integrability and new exact solutions of the \((4 + 1)\)-dimensional Fokas equation
zbMATH Open document ID: 1394.35459
DOI: 10.1155/2015/367425
author: Sheng Zhang
author: Meitong Chen
published in: Mathematical Problems in Engineering
publication date: 2018-08-27T00:00:00Z
review text: Summary: The Painlevé integrability of the \((4 + 1)\)-dimensional Fokas equation is verified by the WTC method of Painlevé analysis combined with a new and more general transformation. By virtue of the truncated Painlevé expansion, two new exact solutions with arbitrary differentiable functions are obtained. Thanks to the arbitrariness of the included functions, the obtained exact solutions not only possess rich spatial structures but also help to bring about two-wave solutions and three-wave solutions. It is shown that the transformation adopted in this work plays a key role in testing the Painlevé integrability and constructing the exact solutions of the Fokas equation.
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 35C05
zbMATH DE Number: 6926162
Wikidata QID: Q59118180
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/367425
OpenAlex ID: W2274473299
cites work: Integrable Nonlinear Evolution Partial Differential Equations in 4 + 2 and<mml:math xmlns:mml="http://www.w3.org/1998/Math/
cites work: Q3995225
cites work: Method for Solving the Korteweg-deVries Equation
cites work: Q4002235
cites work: Exact Solution of the Korteweg—de Vries Equation for Multiple Collisions of Solitons
cites work: Exact solutions for a compound KdV-Burgers equation
cites work: Simplest equation method to look for exact solutions of nonlinear differential equations
cites work: Solitary wave solution for the generalized Kawahara equation
cites work: Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations
cites work: Travelling wave solutions in terms of special functions for nonlinear coupled evolution systems
cites work: The modified extended Fan sub-equation method and its application to the \((2+1)\)-dimensional Broer-Kaup-Kupershmidt equation
cites work: A generalized auxiliary equation method and its application to (2+1)-dimensional asymmetric Nizhnik–Novikov–Vesselov equations
cites work: Exp-function method for nonlinear wave equations
cites work: Variable-coefficient Jacobi elliptic function expansion method for (2+1)-dimensional Nizhnik-Novikov-Vesselov equations
cites work: A further improved extended Fan sub-equation method for \((2+1)\)-dimensional breaking soliton equations
cites work: A generalized new auxiliary equation method and its application to the (2 + 1)-dimensional breaking soliton equations
cites work: A generalized \(F\)-expansion method and new exact solutions of Konopelchenko--Dubrovsky equations
cites work: A transformed rational function method and exact solutions to the \(3+1\) dimensional Jimbo-Miwa equation
cites work: The Painlevé property for partial differential equations
cites work: Q4395062
cites work: On three-dimensional packets of surface waves
cites work: Symmetry Groups and Exact Solutions of New (4+1)-Dimensional Fokas Equation
cites work: EXACT TRAVELING WAVE SOLUTIONS OF A HIGHER-DIMENSIONAL NONLINEAR EVOLUTION EQUATION
cites work: New exact traveling wave solutions of some nonlinear higher-dimensional physical models
cites work: Fractional sub-equation method and its applications to nonlinear fractional PDEs
cites work: New exact solutions for a higher-order wave equation of KdV type using extended F-expansion method
cites work: Exact solutions for \((4 + 1)\)-dimensional nonlinear Fokas equation using extended \(F\)-expansion method and its variant
cites work: A multiple exp-function method for nonlinear differential equations and its application
cites work: Solving the \((3+1)\)-dimensional generalized KP and BKP equations by the multiple exp-function algorithm
cites work: Q4326096
description: scientific article; zbMATH DE number 6926162