Interaction of finite solitons for equations of Born–Infeld type

A class of quasilinear second order partial differential equations with two independent variables is constructed which is in a certain sense a generalization of the Born–Infeld equation. In hyperbolic region all the equations of this class can be reduced to the same canonical system written down in terms of the Riemann invariants. For the class mentioned the Cauchy problem and the problem of interaction of plane finite solitary waves are solved. It is shown that any equation of the class can be transformed into any other equation of the class by means of the Backlund transformation.