Differential invariants for quasi-linear and semi-linear wave-type equations
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摘要
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.
论文关键词:Wave equations,Equivalence transformations,Invariants,Linearization
论文评审过程:Available online 12 February 2008.
论文官网地址:https://doi.org/10.1016/j.amc.2008.01.033