四阶色散非线性薛定谔方程的明暗孤立波和怪波的形成机制  

Study on the generation mechanism of bright and dark solitary waves and rogue wave for a fourth-order dispersive nonlinear Schr?dinger equation

作　　者：李敏 王博婷 许韬 水涓涓 Li Min;Wang Bo-Ting;Xu Tao;Shui Juan-Juan(Department of Mathematics and Physics,North China Electric Power University,Beijing 102206,China;College of Science,China University of Petroleum,Beijing 102249,China)

机构地区：[1]华北电力大学数理学院,北京102206 [2]中国石油大学(北京)理学院,北京102249

出　　处：《物理学报》2020年第1期114-123,共10页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:11705284,61505054);中央高校基本科研业务费专项资金(批准号:2017MS051)~~

摘　　要：本文研究了四阶色散非线性薛定谔方程的明暗孤立波和怪波的形成机制,该模型既可以模拟高速光纤传输系统中超短脉冲的非线性传输和相互作用,又可以描述具有八极与偶极相互作用的一维海森堡铁磁链的非线性自旋激发现象.本文首先通过对四阶色散非线性薛定谔方程的相平面分析,发现由其约化得到的二维平面自治系统具有同宿轨道和异宿轨道,并在相应条件下求得了方程的明孤立波解和暗孤立波解,从而揭示了同异宿轨道和孤立波解的对应关系;其次,基于非零背景平面上的精确一阶呼吸子解,给出了呼吸子的群速度和相速度的显式表达式,进而分析得出呼吸子的速度存在跳跃现象.最后,为了验证在跳跃点处呼吸子可以转化为怪波,将呼吸子解在速度跳跃条件下取极限获得了一阶怪波解,从而证实怪波的产生与呼吸子速度的不连续性有关.In this paper,we study the generation mechanism of bright and dark solitary waves and rogue wave for the fourth-order dispersive nonlinear Schr?dinger(FODNLS)equation,which can not only model the nonlinear propagation and interaction of ultrashort pulses in the high-speed optical fiber transmission system,but also govern the nonlinear spin excitations in the onedimensional isotropic biquadratic Heisenberg ferromagnetic spin with the octupole-dipole interaction.Firstly,via the phase plane analysis,we obtain both the homoclinic and heteroclinic orbits for the two-dimensional plane autonomous system reduced from the FODNLS equation.Further,we derive the bright and dark solitary wave solutions under the corresponding conditions,which reveals the relationship between the homoclinic(heteroclinic)orbit and solitary wave.Secondly,based on the exact first-order breather solution of the FODNLS equation over a nonvanishing background,we give the explicit expressions of group and phase velocities,and reveal that there exists a jump in both the velocities.Finally,in order to verify that the breather becomes a rogue wave at the jumping point,we obtain the firstorder rogue wave solution by taking the limit of the breather solution at such point,which confirms the relationship of the generation of rogue wave with the velocity discontinuity.

关 键 词：同异宿轨道 孤立波 怪波 速度不连续性 

分 类 号：G63[文化科学—教育学]