Open Access

Periodic and Solitary Wave Solutions for the One-Dimensional Cubic Nonlinear Schrödinger Model


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Using a similar approach as Korteweg and de Vries, [19], we obtain periodic solutions expressed in terms of the Jacobi elliptic function cn, [3], for the self-focusing and defocusing one-dimensional cubic nonlinear Schrödinger equations. We will show that solitary wave solutions are recovered through a limiting process after the elliptic modulus of the Jacobi elliptic function cn that describes the periodic solutions for the self-focusing nonlinear Schrödinger model.

eISSN:
1844-0835
Language:
English
Publication timeframe:
1 time per year
Journal Subjects:
Mathematics, General Mathematics