Multisoliton solutions of the Degasperis–Procesi equation and their peakon limit
Multisoliton solutions of the Degasperis–Procesi equation and their peakon limit
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DOI：
10.1088/0266-5611/21/5/004
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发表时间：
2005-10
期刊：
影响因子：
2.1
通讯作者：
Y. Matsuno
中科院分区：
文献类型：
--
作者：
Y. Matsuno
利用Kadomtsev-Petviashvili族多孤子解的约化过程（CKP约化）构造了Degasperis-Procesi（DP）方程的多孤子解.的解决方案有参数表示，并表现出一些新的功能相比，现有的孤子解决方案。特别感兴趣的是一个和两个孤子的解决方案进行了详细的分析。得到了两个孤子相互作用过程中相移的显式表达式。我们发现，孤子的速度依赖于其振幅的非线性，而不是通常的线性关系。另外，两个孤子的相互作用表明，在一定的波参数范围内，慢孤子呈现非负相移。随后，我们考虑孤子解的峰子极限，并表明它恢复了DP方程的峰子解的所有功能。我们还导出了一般N孤子解的渐近形式以及相移公式。
The multisoliton solutions of the Degasperis–Procesi (DP) equation are constructed by means of a reduction procedure (CKP reduction) for the multisoliton solutions of the Kadomtsev–Petviashvili hierarchy. The solutions have parametric representations and exhibit several new features when compared with existing soliton solutions. Of particular interest are the one- and two-soliton solutions for which a detailed analysis is performed. The explicit formula for the phase shift is obtained which occurs in the interaction process of two solitons. We find that the soliton velocity depends nonlinearly on its amplitude as opposed to the usual linear relation. Also, the interaction of two solitons reveals that the slow soliton exhibits a non-negative phase shift in a certain range of the wave parameters. Subsequently, we consider the peakon limit of the soliton solutions and show that it recovers all the features already reported for the peakon solutions of the DP equation. We also derive the asymptotic form of the general N-soliton solution as well as the formula for the phase shift.