Darboux transformation and analytic solutions of the discrete -symmetric nonlocal nonlinear Schrödinger equation

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• 作者：Tao Xu^a ; ^{xutao@cup.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Hengji Li^a ; Hongjun Zhang^a ; Min Li^b ; Sha Lan^a
• 关键词：Nonlocal nonlinear Schrö ; dinger equation ; Soliton solutions ; Darboux transformation ; Parity-time symmetry
• 刊名：Applied Mathematics Letters
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：63
• 期：Complete
• 页码：88-94
• 全文大小：918 K

文摘

In this letter, for the discrete parity-time-symmetric nonlocal nonlinear Schrödinger equation, we construct the Darboux transformation, which provides an algebraic iterative algorithm to obtain a series of analytic solutions from a known one. To illustrate, the breathing-soliton solutions, periodic-wave solutions and localized rational soliton solutions are derived with the zero and plane-wave solutions as the seeds. The properties of those solutions are also discussed, and particularly the asymptotic analysis reveals all possible cases of the interaction between the discrete rational dark and antidark solitons.