Geodesic
Cauchy problem for multidimensional coupled system of nonlinear Schrödinger equation and generalized IMBq equation
Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) no. 1, pp. 15-38

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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 $$ i\varepsilon_t+\nabla^2\varepsilon-u\varepsilon=0, $$ $$ u_{tt}-\nabla^2u-a\nabla^2u_{tt}=\nabla^2f(u)+\nabla^2(|\varepsilon|^2) $$ are proved.
Classification : 35D05, 35K55, 35L35, 35Q55
Keywords: coupled system of nonlinear Schrödinger equation and generalized IMBq; multidimensional; periodic boundary value problem; Cauchy problem; generalized local solution; classical local solution 
@article{CMUC_1998__39_1_a2,
     author = {Guowang, Chen},
     title = {Cauchy problem for multidimensional coupled system of nonlinear {Schr\"odinger} equation and generalized {IMBq} equation},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {15--38},
     publisher = {mathdoc},
     volume = {39},
     number = {1},
     year = {1998},
     mrnumber = {1622316},
     zbl = {0940.35181},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1998__39_1_a2/}
}
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Guowang, Chen. Cauchy problem for multidimensional coupled system of nonlinear Schrödinger equation and generalized IMBq equation. Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) no. 1, pp. 15-38. http://geodesic.mathdoc.fr/item/CMUC_1998__39_1_a2/