Electron. J. Differential Equations, Vol. 2017 (2017), No. 179, pp. 1-15.

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: Zakharov-Shabat system; NLS equation; norming constants; inverse scattering transform.

Show me the PDF file (238 KB), TEX file for this article.

Theresa N. Busse Martines
Department of Mathematics and Statistics
University of the Incarnate Word
San Antonio, TX 78209, USA
email: martines@uiwtx.edu

Return to the EJDE web page