Geodesic
Legendre transformation in Born--Infeld models, Monge--Ampere equation and exact solutions
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 29, Tome 520 (2023), pp. 151-161

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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. 
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     author = {E. Sh. Gutshabash},
     title = {Legendre transformation in {Born--Infeld} models, {Monge--Ampere} equation and exact solutions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
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     publisher = {mathdoc},
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     year = {2023},
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E. Sh. Gutshabash. Legendre transformation in Born--Infeld models, Monge--Ampere equation and exact solutions. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 29, Tome 520 (2023), pp. 151-161. http://geodesic.mathdoc.fr/item/ZNSL_2023_520_a5/