Electron. J. Differential Equations,
Vol. 2017 (2017), No. 179, pp. 115.
Generalized inverse scattering transform for the nonlinear
Schrodinger equation for bound states with higher multiplicities
Theresa N. Busse Martines
Abstract:
We consider a generalization of the inverse scattering transform for
the nonlinear Schrodinger (NLS) equation when bound states
have multiplicities greater than one. This generalization is
accomplished by deriving an explicit compact formula for the time
evolution of the norming constants in the presence of nonsimple bound states.
Such a formula helps to find explicit solutions to the NLS equation and
obtain a generalization of soliton solutions.
Submitted June 123, 2017. Published July 13, 2017.
Math Subject Classifications: 35Q55, 37K15, 35Q51.
Key Words: ZakharovShabat system; NLS equation; norming constants;
inverse scattering transform.
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Theresa N. Busse Martines
Department of Mathematics and Statistics
University of the Incarnate Word
San Antonio, TX 78209, USA
email: martines@uiwtx.edu

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