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

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica

Mucalica Ana¹  Bica Ion¹ 

[1] Department of Mathematics and Statistics, MacEwan University, 10700 104 Ave NW, Edmonton, AB, Canada, T5J 4S2.;

关键词: nls;    self-focusing;    defocusing;    dispersive;    nonlinearity;    carrier waves;    solution profile;    envelope;    cnoidal waves;    solitary waves;    surface gravity waves;    sound waves;    water-air interface;    sonic layer depth;    primary 33e05, 35q55;    secondary 35q53;   

DOI  :  10.2478/auom-2022-0018

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown