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On multi-dimensional partial differential equations with power nonlinearities in first derivatives
О многомерных уравнениях в частных производных со степенными нелинейностями по первым производным
2017
Ufimskii Matematicheskii Zhurnal
О многомерных уравнениях в частных производных со степенными нелинейностями по первым производным
Preserved Fulltext
We consider a class of multi-dimensional partial differential equations involving a linear differential operator of arbitrary order and a power nonlinearity in the first derivatives. Under some additional assumptions for this operator, we study the solutions of multi-dimensional travelling waves that depend on some linear combinations of the original variables. The original equation is transformed to a reduced one, which can be solved by the separation of variables. Solutions of the reduced
doi:10.13108/2017-9-1-98
fatcat:x5zte2n33jbvpngdmgshy6as7y