Multi-dimensional non-autonomous second order equation with power nonlinearities

We consider non-autonomous multi-dimensional partial differential equation of the second order, the right side of which contains arbitrary nonlinearity on the unknown function and power nonlinearities on its first partial derivatives. There is founded the solution of travelling wave type for this equation in the implicit form. There are received the explicit solutions of travelling wave type for the case of power nonlinearity on the unknown function. In particular, these solutions can be in the form of some elementary functions. There are also received the solutions in the form of quadratic polynomial and generalized monomial, and the conditions on the parameters and on the right side of equation are determined, under which these solutions exist. There are founded some solutions, which can be represented through the functions of independent variables subsets, in particular, in the form of sum and production of such functions, and the solutions of aggregated travelling wave type. Also there are received the solutions in the form of linear combination of some exponential functions. The properties of the founded solutions under the different parameters of equation are analysed.