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Classification of the solitary waves in coupled nonlinear Schrödinger equations. (English) Zbl 0938.35180

Summary: The solitary waves in coupled nonlinear Schrödinger equations are classified into infinite families. For each of the first three families, the parameter region is specified and the parameter dependence of its solitary waves is described and explained. We find that the parameter regions of these solution families are novel and irregular, and the parameter dependence of the solitary waves is sensitive. The stability of these families of solitary waves is also determined. We show that only the family of symmetric and single-humped solitary waves is stable.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
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