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Further scattering results for almost cubic nonlinear Schrödinger equation

✍ Scribed by S. Demirbaş; A. Eden

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
250 KB
Volume
24
Category
Article
ISSN
0893-9659

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✦ Synopsis

We present three results on the scattering of solutions for the almost cubic nonlinear Schrödinger equations. When initial datum has a small X p -norm, the solutions scatter in L 2 , when the initial datum is in H s with a small L 2 -norm with 0 ≤ s ≤ 1 then they scatter in H s . Finally, whenever we have global existence of H 1 solutions, we also have scattering in the H 0,1 -norm.

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✍ Abdelhalim Ebaid; S.M. Khaled 📂 Article 📅 2011 🏛 Elsevier Science 🌐 English ⚖ 312 KB

method a b s t r a c t Although, many exact solutions were obtained for the cubic Schrödinger equation by many researchers, we obtained in this research not only more exact solutions but also new types of exact solutions in terms of Jacobi-elliptic functions and Weierstrass-elliptic function.