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

Aiyong Chen | Zendy; Shuangquan Wen | Zendy; Wentao Huang | Zendy

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

Author(s) -

Aiyong Chen,

Shuangquan Wen,

Wentao Huang

Publication year - 2012

Publication title -

journal of applied analysis and computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.55

H-Index - 21

eISSN - 2158-5644

pISSN - 2156-907X

DOI - 10.11948/2012010

Subject(s) - phase portrait , mathematics , mathematical analysis , eigenvalues and eigenvectors , stability (learning theory) , nonlinear system , physics , bifurcation , quantum mechanics , machine learning , computer science

In this paper, we study the existence and orbital stability of periodic wave solutions or the Schrodinger 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.

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