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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.

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

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