We present numerical simulations of a new type of singular solutions of the critical nonlinear Schrödinger equation (NLS), that collapse with a quasi self-similar ring profile at a square root blowup rate. We find and analyze the equation of the ring profile. We observe that the self-similar ring pr
Singularity analysis and explicit solutions of a new coupled nonlinear Schrödinger type equation
✍ Scribed by Xuelin Yong; Jianwei Gao; Zhiyong Zhang
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 279 KB
- Volume
- 16
- Category
- Article
- ISSN
- 1007-5704
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✦ Synopsis
The Painlevé test is performed for a new coupled nonlinear Schrödinger type equation. It is shown that this equation passes the integrability test and is P-integrable. By means of the truncated singular expansions, we construct some novel explicit solutions from the trivial zero solution. Furthermore, the traveling wave solutions are presented by direct quadrature method.
📜 SIMILAR VOLUMES
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.