Implicit similarities and inverse isovector methods
type: Item
instance of: scholarly article
title: Implicit similarities and inverse isovector methods
zbMATH Open document ID: 0563.35009
DOI: 10.1007/BF00250936
author: Dominic G. B. Edelen
published in: Archive for Rational Mechanics and Analysis
publication date: 1983-01-01T00:00:00Z
review text: The group theoretic method, indicated by notions such as contact ideal, isovector field, similarity solution [see \textit{D. G. B. Edelen}, Isovector methods for Equations of Balance. With programs for computer assistance in operator calculations and an exposition of practical topics of the exterior calculus (1980; Zbl 0452.58001)], is applied to a system of second order p.d.e.'s in two independent and two dependent variables, which may be described by the balance 2-forms \[ (*)\quad B_{\alpha}=F^ 0_{\alpha}dx^ 1\wedge dx^ 2-d(F^ 1_{\alpha}dx^ 2-F^ 2_{\alpha}dx^ 1) \] with given functions \(F^ a_{\alpha}=F^ a_{\alpha}(x^ i,q^{\alpha},q^{\alpha}_{x_ i})\); i,\(\alpha\in \{1,2\}.\) The main part of the paper is an illustration by example of the inverse isovector problem: To find (all systems (*), whose balance ideal admits as an isovector field the prolongation of the vector field \(-x^ 1\partial /dx^ 1+(1-2q^ 1)\partial /\partial x^ 2+q^ 1\partial /\partial q^ 1+x^ 1\partial /\partial q^ 2\). This example and the corresponding reduction of (*) to a system of o.d.e.'s is carried out in detail, with special emphasis on the fact that the similarity variables occurring here are functions of the original independent and dependent variables as well.
Mathematics Subject Classification ID: 35A25
Mathematics Subject Classification ID: 35A30
Mathematics Subject Classification ID: 58A10
zbMATH DE Number: 3897422
zbMATH Keywords: similarity solution
zbMATH Keywords: ideal of differential forms
zbMATH Keywords: group theoretic method
zbMATH Keywords: inverse isovector problem
zbMATH Keywords: similarity variables
MaRDI profile type: Publication
cites work: Geometric Approach to Invariance Groups and Solution of Partial Differential Systems
cites work: Similarity methods for differential equations
cites work: Q3280274
description: scientific article; zbMATH DE number 3897422