Differential invariants for quasi-linear and semi-linear wave-type equations
The quasi-linear wave equation \(u_{tt}=f(t,x,u)u_{xx}+g(t,x,u,u_t,u_x)\) is investigated by group-theoretic method. The authors derive some differential invariants for a class of the equations of the above type, and use them to give a linearization test, i.e. solving equivalence with simplest linear hyperbolic or elliptic equations.
scientific article; zbMATH DE number 5318711
scientific article