EXISTENCE AND ORBITAL STABILITY OF PERIODIC WAVE SOLUTIONS FOR THE NONLINEAR SCHR&#214;DINGER EQUATION

Aiyong Chen; Shuangquan Wen; Wentao Huang

doi:10.11948/2012010

2012 Volume 2 Issue 2

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Aiyong Chen, Shuangquan Wen, Wentao Huang. EXISTENCE AND ORBITAL STABILITY OF PERIODIC WAVE SOLUTIONS FOR THE NONLINEAR SCHRÖDINGER EQUATION[J]. Journal of Applied Analysis & Computation, 2012, 2(2): 137-148. doi: 10.11948/2012010

Citation:

Aiyong Chen, Shuangquan Wen, Wentao Huang. EXISTENCE AND ORBITAL STABILITY OF PERIODIC WAVE SOLUTIONS FOR THE NONLINEAR SCHRÖDINGER EQUATION[J]. Journal of Applied Analysis & Computation, 2012, 2(2): 137-148. doi: 10.11948/2012010

EXISTENCE AND ORBITAL STABILITY OF PERIODIC WAVE SOLUTIONS FOR THE NONLINEAR SCHRÖDINGER EQUATION

1 School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, 541004, China;
2 Center of Nonlinear Science Studies, Kunming University of Science and Technology, Kunming, 650093, China

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Abstract

Abstract

In this paper, we study the existence and orbital stability of periodic wave solutions for the Schrödinger equation. The existence of periodic wave solution is obtained by using the phase portrait analytical technique. The stability approach is based on the theory developed by Angulo for periodic eigenvalue problems. A crucial condition of orbital stability of periodic wave solutions is proved by using qualitative theory of ordinal differential equations. The results presented in this paper improve the previous approach, because the proving approach does not dependent on complete elliptic integral of first kind and second kind.
- Schrödinger equation /
- orbital stability /
- periodic wave solution /
- Picard-Fuchs equattion
MSC: 35Q51;35Q53

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References

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