# American Institute of Mathematical Sciences

September  2011, 16(2): 507-527. doi: 10.3934/dcdsb.2011.16.507

## Traveling wave solutions and its stability for 3D Ginzburg-Landau type equation

 1 School of Mathematics and Systems Science & LMIB, Beijing University of Aeronautics and Astronautics, Beijing, 100191, China 2 Department of Mechanical Engineering, Zhejiang University, Hangzhou 310027, China 3 School of Mathematics and Systems Science, Beijing University of Aeronautics-Astronautics, Beijing 100191, China, China, China

Received  February 2010 Revised  December 2010 Published  June 2011

In this paper, a three dimensional Ginburg-Landau type equation is considered. Firstly, two families of new traveling wave solutions in term of explicit functions are presented by using the homogeneous balance method, in which one consists of variable-amplitude solutions and the other constant-amplitude solutions (namely, plane wave solutions). Moreover, the stability of plane wave solutions is analyzed by using the regular phase plane techniques.
Citation: Shujuan Lü, Chunbiao Gan, Baohua Wang, Linning Qian, Meisheng Li. Traveling wave solutions and its stability for 3D Ginzburg-Landau type equation. Discrete & Continuous Dynamical Systems - B, 2011, 16 (2) : 507-527. doi: 10.3934/dcdsb.2011.16.507
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