This paper is concerned with the study of the Cauchy problem associated with an -dimensional generalized Benney-Luke equation, , where . We prove the existence and the uniqueness of the global solution of the Cauchy problem for the case by using energy conservation law and give the existence and the nonexistence of the global solution of the Cauchy problem for the case by constructing the stable set and the unstable set.
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© 2007 American Institute of Physics.
2007
American Institute of Physics
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