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Solutions of the Nonlinear Wave Equation utt=(uux)x Invariant under Conditional Symmetries

M. Foursov
Evgenii M. Vorob'ev
Journal / Anthology

Journal of Physics A
Year: 1996
Volume: 29
Page range: 6363-6373

In this paper we discuss the application of conditional symmetries for obtaining exact and approximate solutions of the equation utt=(uux)x.. We propose to use the invariance properties of the infinitesimal conditional symmetries with respect to the classical Lie symmetries in order to explicitly solve the determining equations for the conditional symmetries. Exact solutions invariant under the conditional symmetries are given by explicit formulae, approximate solutions are calculated and presented in the graphical form by using 'Mathematica'.

*Mathematics > Calculus and Analysis > Differential Equations