A note on new solitary and similarity class of solutions of a fourth-order non-linear evolution equation
type: Item
instance of: scholarly article
title: A note on new solitary and similarity class of solutions of a fourth-order non-linear evolution equation
zbMATH Open document ID: 1156.35399
author: Alfred Huber
published in: Applied Mathematics and Computation
publication date: 2008-09-05T00:00:00Z
review text: The author analyzes the algebraic properties of solutions of the nonlinear equation \[ \frac{\partial^{2}U}{\partial {t^{2}}}+\frac{\partial^{4}U}{\partial{x^{3}}\partial t}+ 3\frac{\partial^{2}U}{\partial{x^{2}}}\frac{\partial^{2}U}{\partial x \partial t}=0,\quad t>0 \] using the properties of the ordinary differential equation obtained by the transform \[ U(x,t)=f(\xi),\quad \text{with} \quad \xi=x-\lambda t. \]
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 34A25
Mathematics Subject Classification ID: 34C30
Mathematics Subject Classification ID: 35C05
zbMATH DE Number: 5321670
zbMATH Keywords: Lie group formalism
zbMATH Keywords: similarity solutions
zbMATH Keywords: manifolds of solutions
zbMATH Keywords: solitary class of solutions
reviewed by: Ivan Secrieru
MaRDI profile type: Publication
full work available at URL: j.amc.2008.03.032
OpenAlex ID: W2026272467
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cites work: On class of solutions of nonlinear partial differential equation of sixth order generated by a classical and non-classical symmetry analysis
DOI: 10.1016/J.AMC.2008.03.032
description: scientific article; zbMATH DE number 5321670