A new integrable equation with no smooth solitons
A new integrable equation with no smooth solitons
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DOI：
10.1016/j.chaos.2007.11.034
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发表时间：
2009-07
影响因子：
7.8
通讯作者：
Z. Qiao;Liping Liu
中科院分区：
文献类型：
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作者：
Z. Qiao;Liping Liu
在本文中，我们提出了一个新的完全可积方程：它没有光滑孤子。该方程具有双哈密顿结构和Lax对，这意味着方程可积。通过研究这个新方程，我们在非齐次边界条件 lim|x|→∞m=B 下开发了两种新的孤子解，其中 B 是非零常数。一种是连续、分段平滑的“W/M”形峰孤立解，另一种是单峰孤子解。这两种新的峰值孤子不能写成常规类型peakon：ce-|x-ct|，其中c是常数。我们将提供图表来显示这些新型峰值孤子。
In this paper, we propose a new completely integrable equation:which has no smooth solitons. This equation is shown to have bi-Hamiltonian structure and Lax pair, which imply integrability of the equation. Studying this new equation, we develop two new kinds of soliton solutions under the inhomogeneous boundary condition lim|x|→∞m=B where B is nonzero constant. One is continuous and piecewise smooth “W/M”-shape-peaks solitary solution and the other one-single-peak soliton. The two new kinds of peaked solitons can not be written as the regular type peakon: ce-|x-ct|, where c is a constant. We will provide graphs to show those new kinds of peaked solitons.