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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On integrability of nonautonomous nonlinear Schrödinger equations


Author: Sergei K. Suslov
Journal: Proc. Amer. Math. Soc. 140 (2012), 3067-3082
MSC (2010): Primary 35Q55, 35Q51; Secondary 35P30, 81Q05
Published electronically: December 30, 2011
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Abstract: We show, in general, how to transform the nonautonomous nonlinear Schrödinger equation with quadratic Hamiltonians into the standard autonomous form that is completely integrable by the familiar inverse scattering method in nonlinear science. Derivation of the corresponding equivalent nonisospectral Lax pair is also outlined. A few simple integrable systems are discussed.


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Additional Information

Sergei K. Suslov
Affiliation: School of Mathematical and Statistical Sciences and the Mathematical, Computational and Modeling Sciences Center, Arizona State University, Tempe, Arizona 85287–1804
Email: sks@asu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11176-6
PII: S 0002-9939(2011)11176-6
Keywords: Nonlinear Schrödinger equations, generalized harmonic oscillators, Green’s function, propagator, completely integrable systems, Lax pair, Zakharov–Shabat system.
Received by editor(s): March 18, 2011
Published electronically: December 30, 2011
Communicated by: Ken Ono
Article copyright: © Copyright 2011 American Mathematical Society