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Imaginary eigenvalues of Zakharov-Shabat problems with non-zero background. (English) Zbl 1404.35402

Summary: The focusing Zakharov-Shabat scattering problem on the infinite line with non-zero boundary conditions for the potential is studied, and sufficient conditions on the potential are identified to ensure that the problem admits only purely imaginary discrete eigenvalues. The results, which generalize previous work by M. Klaus and J. K. Shaw [“Purely imaginary eigenvalues of Zakharov-Shabat systems”, Phys. Rev. E 65, No. 3, Article ID 036607, 5 p. (2002; doi:10.1103/physreve.65.036607); SIAM J. Math. Anal. 34, No. 4, 759–773 (2003; Zbl 1034.34097)], are applicable to the study of solutions of the focusing nonlinear Schrödinger equation with non-zero background.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
47J10 Nonlinear spectral theory, nonlinear eigenvalue problems

Citations:

Zbl 1034.34097
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Full Text: DOI

References:

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