Abstract: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 Schr\"odinger 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.
Keywords: coupled system of nonlinear Schr\"odinger equation and generalized IMBq, multidimensional, periodic boundary value problem, Cauchy problem, generalized local solution, classical local solution
AMS Subject Classification: 35L35, 35K55