Geodesic
On solutions of the Monge--Ampere equation with power-law non-linearity with respect to first derivatives
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 4 (2016), pp. 33-43

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In this work, the two-dimensional Monge–Ampere equation the right-hand side of which includes arbitrary non-linearity with respect to the unknown function and power-law nonlinearity with respect to its first derivatives is considered. To solve this equation, the method of functional separation of variables is used. We study the case when one of the unknown functions used in the method of separation of variables is linear and also the case when all these functions are arbitrary. The exact solutions in the implicit form of the considered equation are received in the presence of arbitrary nonlinearity with respect to the unknown function. For the case when the equation does not contain unknown function explicitly, its solutions are found in an explicit form. The solutions have been analyzed for different values of parameters characterizing the nonlinearity.
Keywords: Monge–Ampere equation, functional separation of variables, power-law non-linearity. 
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     author = {I. V. Rakhmelevich},
     title = {On solutions of the {Monge--Ampere} equation with power-law non-linearity with respect to first derivatives},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {33--43},
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I. V. Rakhmelevich. On solutions of the Monge--Ampere equation with power-law non-linearity with respect to first derivatives. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 4 (2016), pp. 33-43. http://geodesic.mathdoc.fr/item/VTGU_2016_4_a3/