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On smooth solutions to the initial value problem for the mixed nonlinear Schrödinger equations*

Published online by Cambridge University Press:  14 November 2011

Guo Boling  and
Tan Shaobin
Guo Boling
Affiliation:
Centre for Nonlinear Studies, Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing, China
Tan Shaobin
Affiliation:
Centre for Nonlinear Studies, Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing, China
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Synopsis

Solutions to the initial value problem for the mixed nonlinear Schrödinger equation

are considered. Conditions on the constants α,β, γ, function g(·) and initial data u(x, 0) are given so that, for this problem, the unique existence of smooth solutions is proved. In addition, the decay behaviours of the smooth solutions as |x|→+∞ are discussed.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 119 , Issue 1-2 , 1991 , pp. 31 - 45
Copyright
Copyright © Royal Society of Edinburgh 1991

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