Asymptotic analysis of the Marchenko integral equation and soliton asymptotics of a solution of the nonlinear schrödinger equation
✍ Scribed by Vladimir P. Kotlyarov
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 354 KB
- Volume
- 87
- Category
- Article
- ISSN
- 0167-2789
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This paper deals with the equation Here, u is a complex-valued function of (t, x) # R\_R n , n 2, and \* is a real number. If u 0 is small in L 2, s with s>(nÂ2)+2, then the solution u(t) behaves asymptotically as uniformly in R n as t Ä . Here , is a suitable function called the modified scatteri
## Abstract We are interested in the asymptotic behavior of solutions of a Schrödinger‐type equation with oscillating potential which was studied by A. Its. Here we use a different technique, based on Levinson's Fundamental Lemma, to analyze the asymptotic behavior, and our approach leads to a comp