Dynamics of soliton solutions of the nonlocal Kundu-nonlinear Schrödinger equation.

Dynamics of soliton solutions of the nonlocal Kundu-nonlinear Schrödinger equation.
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DOI：
10.1063/1.5080921
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发表时间：
2019-02
期刊：
Chaos
影响因子：
2.9
通讯作者：
Xujie Shi;Jie Li;Chengfa Wu
Xujie Shi;Jie Li;Chengfa Wu
中科院分区：
数学2区
文献类型：
--
作者：
Xujie Shi;Jie Li;Chengfa Wu

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本文研究了非局部Kundu非线性薛定谔方程，该方程可以通过约化耦合Kundu非线性薛定谔系统得到。在分析本征函数的基础上，构造了一个Riemann-Hilbert问题，导出了耦合Kundu-NLS系统的N孤子解。然后根据散射数据选择适当的对称关系，推导出非局域Kundu-NLS方程的N-孤立子解。研究了非局域Kundu-NLS方程中孤子的动力学行为。对于单孤子，给出了规范函数对孤子的影响。与局域Kundu-NLS方程中的双孤子动力学行为相比，非局域Kundu-NLS方程中的双孤子动力学行为表现出许多不同之处。重复坍缩是奇异孤子的一个共同特征，有些奇异孤子似乎不是单孤子的叠加。奇异孤子在谱空间中不同的本征值配置下表现出不同的行为。此外，根据这些特征值配置，给出了三种有界解。此外，还给出了两类退化解，特别是对正子解进行了详细的讨论。分析了位置解的分解，并近似给出了位置解的轨迹。
In this paper, we investigate the nonlocal Kundu-nonlinear Schrödinger (Kundu-NLS) equation, which can be obtained from the reduction of the coupled Kundu-NLS system. Based on the analysis of the eigenfunctions, a Riemann-Hilbert problem is constructed to derive the N-soliton solutions of the coupled Kundu-NLS system. The N-soliton solutions of the nonlocal Kundu-NLS equation are then deduced with properly chosen symmetry relations on the scattering data. The dynamics of the solitons in the nonlocal Kundu-NLS equation are explored. The impact of the gauge function on the solitons is displayed for one-solitons. Compared with the dynamics of the two-solitons in the local Kundu-NLS equation, the two-solitons in the nonlocal Kundu-NLS equation display many differences. The repeated collapsing is a common feature of the singular solitons, and it seems that some of them are not the superposition of one-solitons. The singular solitons exhibit various behaviors in different eigenvalue configurations in the spectral space. Besides that, three kinds of bounded solutions are presented according to these eigenvalue configurations. In addition, two kinds of degenerate solutions are presented, and in particular, the positon solutions are discussed in detail. The decomposition of the positon solutions is analyzed and their trajectories are given approximately.