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Reciprocal transformation for one‐dimensional conservation equations
Journal article   Peer reviewed

Reciprocal transformation for one‐dimensional conservation equations

Gerald Rosen
Journal of mathematical physics, v 24(4), pp 793-794
Apr 1983

Abstract

one−dimensional systems symmetry transformations Partial Differential Equations
One‐dimensional conservation equations (OCE) of the form ∂n/∂t+∂f/∂x=0 with n=n(x,t)>0 and f=f(n,∂n/∂x, ∂2 n/∂x 2,⋅⋅⋅) admit a symmetric r e c i p r o c a l t r a n s f o r m a t i o n x→x*(x,t), n→n*(x*,t)≡n − 1, f→f*≡−n − 1 f, which produces an equivalent OCE for n* in x* space. Certain OCE of contemporary interest are r e c i p r o c a l i n v a r i a n t in the sense that f*=f(n*, ∂n*/∂x*, ∂2 n*/∂x*2,⋅⋅⋅). There also exists a class of essentially nonlinear OCE for which the reciprocal transformation produces a linear OCE, and thus equations in this class are solvable analytically.

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Web of Science research areas
Physics, Mathematical
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