Solitons, breathers and rogue waves for a sixth-order variable-coefficient nonlinear Schrödinger equation in an ocean or optical fiber
Solitons, breathers and rogue waves for a sixth-order variable-coefficient nonlinear Schrödinger equation in an ocean or optical fiber
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DOI：
10.1140/epjp/i2017-11318-y
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发表时间：
2017-01
期刊：
影响因子：
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通讯作者：
Shu-Liang Jia;Yi-Tian Gao;Chen Zhao;Zhong-Zhou Lan;Yu-Jie Feng
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文献类型：
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作者：
Shu-Liang Jia;Yi-Tian Gao;Chen Zhao;Zhong-Zhou Lan;Yu-Jie Feng
本文研究了海洋或光纤中的六阶变系数非线性Schrödinger方程。通过达布变换（DT）和广义DT，我们得到了多孤子解、呼吸波解和异常波解。我们分别选取三阶、四阶、五阶和六阶色散系数(x)、(x)、(x)和(x)的不同值，研究它们对这些解的影响，其中存在缩放传播变量。选取(x)、(x)、(x)和(x)作为线性、抛物和周期函数，分别得到抛物、三次和拟周期孤子。给出了两个孤子之间的正向和超车相互作用，并且这种相互作用是弹性的。此外，当谱参数一定时，两个孤子之间出现激波区，相互作用是非弹性的。研究了两种呼吸波之间的相互作用，发现其相互作用区域与二阶异常波的相互作用区域相似。当(x)、(x)、(x)和(x)为周期函数或奇数函数时，将异常波分解为若干一阶异常波。
Under investigation in this paper is a sixth-order variable-coefficient nonlinear Schrödinger equation in an ocean or optical fiber. Through the Darboux transformation (DT) and generalized DT, we obtain the multi-soliton solutions, breathers and rogue waves. Choosing different values of(x),(x),(x) and(x), which are the coefficients of the third-, fourth-, fifth- and sixth-order dispersions, respectively, we investigate their effects on those solutions, wherexis the scaled propagation variable. When(x),(x),(x) and(x) are chosen as the linear, parabolic and periodic functions, we obtain the parabolic, cubic and quasi-periodic solitons, respectively. Head-on and overtaking interactions between the two solitons are presented, and the interactions are elastic. Besides, with certain values of the spectral parameter, a shock region between the two solitons appears, and the interaction is inelastic. Interactions between two kinds of the breathers are also studied, and we find that the interaction regions are similar to those of the second-order rogue waves. Rogue waves are split into some first-order rogue waves when(x),(x),(x) and(x) are the periodic or odd-numbered functions.