Legendre transformation in Born–Infeld models, Monge–Ampere equation and exact solutions

Gutshabash E. Sh. Legendre transformation in Born–Infeld models, Monge–Ampere equation and exact solutions. Exact solutions of the equation obtained by applying the Legendre transformation to the Born–Infeld equation are constructed, and the quasilinear system arising in connection with this transformation is investigated. Based on the linearization of the Monge–Ampere equation, some of its particular solutions are calculated.