On Solutions of an Extended Nonlocal Nonlinear Schrödinger Equation in Plasmas

Yehui Huang, Hongqing Jing, Min Li, Zhenjun Ye and Yuqin Yao
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Yehui Huang: School of Mathematics and Physics, North China Electric Power University, Beijing 100083, China
Hongqing Jing: School of Mathematics and Physics, North China Electric Power University, Beijing 100083, China
Min Li: School of Mathematics and Physics, North China Electric Power University, Beijing 100083, China
Zhenjun Ye: School of Mathematics and Physics, North China Electric Power University, Beijing 100083, China
Yuqin Yao: Department of Applied Mathematics, China Agricultural University, Beijing 100083, China

Mathematics, 2020, vol. 8, issue 7, 1-15

Abstract: The parity-time symmetric nonlocal nonlinear Schrödinger equation with self-consistent sources (PTNNLSESCS) is used to describe the interaction between an high-frequency electrostatic wave and an ion-acoustic wave in plasmas. In this paper, the soliton solutions, rational soliton solutions and rogue wave solutions are derived for the PTNNLSESCS via the generalized Darboux transformation. We find that the soliton solutions can exhibit the elastic interactions of different type of solutions such as antidark-antidark, dark-antidark, and dark-dark soliton pairs on a continuous wave background. Also, we discuss the degenerate case in which only one antidark or dark soliton remains. The rogue wave solution is derived in some specially chosen situations.

Keywords: parity-time symmetric; generalized Darboux transformation; soliton solution; rational solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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