Ufa Mathematical Journal
    Volume 9, Number 1, pp. 98-108

    On multi-dimensional partial differential equations with power nonlinearities in first derivatives

    Rakhmelevich I.V.


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    We consider a class of multidimensional partial differential equations involving a linear differential operator of arbitrary order and power nonlinearity in the first derivatives. Under some additional assumptions for this operator, we study the solutions of multidimensional 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 separation of variables. Solutions of the reduced equation are found for the cases of additive, multiplicative and combined separation of variables.