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Keywords:
coupled system of nonlinear Schrödinger equation and generalized IMBq; multidimensional; periodic boundary value problem; Cauchy problem; generalized local solution; classical local solution
coupled system of nonlinear Schrödinger equation and generalized IMBq; multidimensional; periodic boundary value problem; Cauchy problem; generalized local solution; classical local solution
Summary:
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 $$ i\varepsilon_t+\nabla^2\varepsilon-u\varepsilon=0, $$ $$ u_{tt}-\nabla^2u-a\nabla^2u_{tt}=\nabla^2f(u)+\nabla^2(|\varepsilon|^2) $$ are proved.
References:
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