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Solitons and breathers for a generalized nonlinear Schrödinger equation via the binary Bell polynomials
Mathematics and Computers in Simulation ( IF 4.6 ) Pub Date : 2021-01-01 , DOI: 10.1016/j.matcom.2020.07.020
Yan Jiang , Qi-Xing Qu

Abstract In this paper, we investigate a generalized nonlinear Schrodinger equation with two certain terms in the single-mode optical fibers. Via the binary Bell polynomials, a more general bilinear form and analytic solutions are obtained. On the basis of those solutions, we present the parametric regions for the existence of the solitons and breathers on a nonzero background. From the soliton solutions, we prove the soliton interaction to be elastic through the asymptotic analysis. The interactions can be observed between (i) two dark solitons, (ii) two anti-dark solitons, and (iii) one dark and one anti-dark solitons, and relevant parametric conditions of the three types of interactions are given. From the breather solutions, the general breathers, Akhmediev breathers and Kuznetsov–Ma breathers can be respectively derived with the different parametric conditions. Besides, we obtain some rational solutions by taking the limit of the breather solutions. Based on those rational solutions, the parametric conditions for the soliton interactions and rogue waves are given.

中文翻译:

基于二元贝尔多项式的广义非线性薛定谔方程的孤子和呼吸器

摘要 在本文中,我们研究了单模光纤中具有两个确定项的广义非线性薛定谔方程。通过二元贝尔多项式,可以获得更一般的双线性形式和解析解。在这些解决方案的基础上,我们提出了在非零背景上存在孤子和呼吸器的参数区域。从孤子解中,我们通过渐近分析证明孤子相互作用是弹性的。可以观察到(i)两个暗孤子,(ii)两个反暗孤子和(iii)一个暗和一个反暗孤子之间的相互作用,并给出了三​​种相互作用的相关参数条件。从呼吸器解决方案,一般呼吸器,Akhmediev 呼吸器和 Kuznetsov-Ma 呼吸器可以通过不同的参数条件分别导出。此外,我们通过取呼吸器解的极限得到一些合理的解。基于这些合理的解决方案,给出了孤子相互作用和流氓波的参数条件。
更新日期:2021-01-01
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