Wave fronts and cascades of soliton interactions in the periodic two dimensional Volterra system
Wave fronts and cascades of soliton interactions in the periodic two dimensional Volterra system
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DOI：
10.1016/j.physd.2017.01.003
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发表时间：
2017-05-15
影响因子：
4
通讯作者：
Wang, Jing Ping
中科院分区：
文献类型：
--
作者：
Bury, Rhys;Mikhailov, Alexander V.;Wang, Jing Ping
本文发展了周期为N的二维周期沃尔泰拉系统的dressing方法。我们导出了任意秩k的孤子解，并给出了秩1解的完整分类。我们已经找到了一类新的精确解对应的波前表示光滑的界面之间的两个非线性周期波或周期波和平凡（零）的解决方案。波前是非平稳的，并且它们以恒定的平均速度传播。该系统也有类似呼吸子的孤子解，这类似于KP理论中的孤子网。我们将孤子解的分类与Grassmannian算子Gr（R）（k，N）和Gr（C）（k，N）的Schubert分解联系起来. (C)2017作者由爱思唯尔公司出版。这是一篇开放获取的文章，使用CC BY许可证（http：//creativecommons.org/licenses/by/4.0/）。
In the paper we develop the dressing method for the solution of the two-dimensional periodic Volterra system with a period N. We derive soliton solutions of arbitrary rank k and give a full classification of rank 1 solutions. We have found a new class of exact solutions corresponding to wave fronts which represent smooth interfaces between two nonlinear periodic waves or a periodic wave and a trivial (zero) solution. The wave fronts are non-stationary and they propagate with a constant average velocity. The system also has soliton solutions similar to breathers, which resembles soliton webs in the KP theory. We associate the classification of soliton solutions with the Schubert decomposition of the Grassmannians Gr(R)(k, N) and Gr(C)(k, N). (C) 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).