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coupled system of nonlinear Schrödinger equation and generalized IMBq; multidimensional; periodic boundary value problem; Cauchy problem; generalized local solution; classical local solution
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.
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