Differential invariants for quasi-linear and semi-linear wave-type equations
SourceApplied Mathematics and Computation
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In this paper, we consider the class of wave-type equations utt = f (x, t, u) uxx + g (x, t, u, ux, ut) and two special cases of it. We derive the equivalence transformations for these equations and using these transformations, we obtain differential invariants and invariant equations. We employ these invariants or/and invariant equations to classify all equations of this general class that can be mapped into a simple linear hyperbolic or into an elliptic equation. Additional applications are presented. © 2008 Elsevier Inc. All rights reserved.
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