Premium
Rational and semi‐rational solutions of a nonlocal (2 + 1)‐dimensional nonlinear Schrödinger equation
Author(s) -
Peng WeiQi,
Tian ShouFu,
Zhang TianTian,
Fang Yong
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5792
Subject(s) - breather , mathematics , invertible matrix , rogue wave , nonlinear schrödinger equation , bilinear interpolation , mathematical analysis , nonlinear system , integrable system , limit (mathematics) , mathematical physics , bilinear form , rational function , soliton , schrödinger equation , pure mathematics , physics , quantum mechanics , statistics
We consider the fully parity‐time ( P T ) symmetric nonlocal (2 + 1)‐dimensional nonlinear Schrödinger (NLS) equation with respect to x and y . By using Hirota's bilinear method, we derive the N ‐soliton solutions of the nonlocal NLS equation. By using the resulting N ‐soliton solutions and employing long wave limit method, we derive its nonsingular rational solutions and semi‐rational solutions. The rational solutions act as the line rogue waves. The semi‐rational solutions mean different types of combinations in rogue waves, breathers, and periodic line waves. Furthermore, in order to easily understand the dynamic behaviors of the nonlocal NLS equation, we display some graphics to analyze the characteristics of these solutions.