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Advances in Mathematical Physics
Volume 2015, Article ID 408630, 16 pages
http://dx.doi.org/10.1155/2015/408630
Research Article

Explicit Wave Solutions and Qualitative Analysis of the (1 + 2)-Dimensional Nonlinear Schrödinger Equation with Dual-Power Law Nonlinearity

1Department of Physics, Honghe University, Mengzi, Yunnan 661100, China
2College of Mathematics, Honghe University, Mengzi, Yunnan 661100, China

Received 5 July 2015; Revised 30 August 2015; Accepted 31 August 2015

Academic Editor: Giorgio Kaniadakis

Copyright © 2015 Qing Meng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The (1 + 2)-dimensional nonlinear Schrödinger equation with dual-power law nonlinearity is studied using the factorization technique, bifurcation theory of dynamical system, and phase portraits analysis. From a dynamic point of view, the existence of smooth solitary wave, and kink and antikink waves is proved and all possible explicit parametric representations of these waves are presented.