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Laplace transformation and nonlinear hyperbolic equations. (Russian. English summary) Zbl 1240.35344

Pairs of nonlinear equations \[ u_{xy}=f(x, y, u, u_{x}, u_{y}), \, \, q_{xy}=F(x, y, q, q_{x}, q_{y}) \] are described, the linearizations of which are connected through Laplace transformations of the first and second orders. It is shown how the Laplace transformations can be used for the finding of Bäcklund transformations connecting the solutions of nonlinear equations.

MSC:

35L55 Higher-order hyperbolic systems
44A10 Laplace transform
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