On a class of quasilinear hyperbolic reducible systems allowing for special wave interactions
type: Item
instance of: scholarly article
title: On a class of quasilinear hyperbolic reducible systems allowing for special wave interactions
zbMATH Open document ID: 0645.76081
DOI: 10.1007/BF00946339
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1987-01-01T00:00:00Z
review text: For hyperbolic \(2\times 2\)-systems \(y_ t=A(y)y_ x\), the authors show how to construct explicit solutions in the hodograph plane, under the key assumption that two second order partial differential equations involving the left and right eigenvectors and associated eigenvalues of A hold identically. This technique is then used to construct solutions of initial value problems and to show that two smooth localized wave solutions of such an equation that travel in opposite directions will always emerge unchanged (with a phase shift) from their interaction. Examples for systems with the property mentioned above include the problem \(y_{tt}=F^ 2(y_ x,y)y_{xx}\) and a system from isentropic fluid dynamics, for a five parameter class of pressure - density relations.
reviewed by: Hans Engler
Mathematics Subject Classification ID: 76N10
Mathematics Subject Classification ID: 35L60
Mathematics Subject Classification ID: 35C15
zbMATH DE Number: 4053236
zbMATH Keywords: explicit solutions
zbMATH Keywords: hodograph plane
zbMATH Keywords: eigenvectors
zbMATH Keywords: initial value problems
zbMATH Keywords: smooth localized wave solutions
zbMATH Keywords: isentropic fluid dynamics
author: C. Curró
author: D. Fusco
MaRDI profile type: Publication
cites work: Q5801144
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cites work: Large amplitude waves in bounded media I. Reflexion and transmission of large amplitude shockless pulses at an interface
full work available at URL: https://doi.org/10.1007/bf00946339
OpenAlex ID: W2079316875
description: scientific article; zbMATH DE number 4053236