𝔖 Bobbio Scriptorium
✦   LIBER   ✦

New soliton and periodic solutions of (1 + 2)-dimensional nonlinear Schrödinger equation with dual-power law nonlinearity

✍ Scribed by Li-Hua Zhang; Jian-Guo Si

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
583 KB
Volume
15
Category
Article
ISSN
1007-5704

No coin nor oath required. For personal study only.

✦ Synopsis

With the aid of symbolic computation, the new generalized algebraic method is extended to the (1 + 2)-dimensional nonlinear Schrödinger equation (NLSE) with dualpower law nonlinearity for constructing a series of new exact solutions. Because of the dual-power law nonlinearity, the equation cannot be directly dealt with by the method and require some kinds of techniques. By means of two proper transformations, we reduce the NLSE to an ordinary differential equation that is easy to solve and find a rich variety of new exact solutions for the equation, which include soliton solutions, combined soliton solutions, triangular periodic solutions and rational function solutions. Numerical simulations are given for a solitary wave solution to illustrate the time evolution of the solitary creation. Finally, conditional stability of the solution in Lyapunov's sense is discussed.

📜 SIMILAR VOLUMES

Topological 1-soliton solution of the no
Topological 1-soliton solution of the nonlinear Schrodinger’s equation with Kerr law nonlinearity in 1 + 2 dimensions
✍ Anjan Biswas 📂 Article 📅 2009 🏛 Elsevier Science 🌐 English ⚖ 139 KB

In this paper, the topological 1-soliton solution of the nonlinear Schrödinger's equation in 1 + 2 dimensions is obtained by the solitary wave ansatze method. These topological solitons are studied in the context of dark optical solitons. The type of nonlinearity that is considered is Kerr type.