Local solvability of some classes of linear and nonlinear partial differential equations.

Popivanov, P.R.

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The existence, uniqueness and regularity of the generalized local solution and the classical local solution to the periodic boundary value problem and Cauchy problem for the multidimensional coupled system of a nonlinear complex Schrödinger equation and a generalized IMBq equation $i ε_{t} + \nabla^{2} ε - u ε = 0,$ $u_{t t} - \nabla^{2} u - a \nabla^{2} u_{t t} = \nabla^{2} f (u) + \nabla^{2} {(| ε |}^{2})$ are proved.