Soliton solutions to systems of coupled Schrödinger equations of Hamiltonian type

Sirakov, Boyan; Soares, Sérgio

doi:10.1090/S0002-9947-2010-04982-7

Soliton solutions to systems of coupled Schrödinger equations of Hamiltonian type
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by Boyan Sirakov and Sérgio H. M. Soares

Trans. Amer. Math. Soc. 362 (2010), 5729-5744

DOI: https://doi.org/10.1090/S0002-9947-2010-04982-7

Published electronically: May 27, 2010

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Abstract:

We study the existence of positive solutions of Hamiltonian-type systems of second-order elliptic PDE in the whole space. The systems depend on a small parameter and involve a potential having a global well structure. We use dual variational methods, a mountain-pass type approach and Fourier analysis to prove positive solutions exist for sufficiently small values of the parameter.

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