Abstract
In this paper, we consider the class of wave-type equations u tt = f ( x , t , u ) u xx + g ( x , t , u , u x , u t ) 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.
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