A two-component generalization of the reduced Ostrovsky equation and its integrable semi-discrete analogue
A two-component generalization of the reduced Ostrovsky equation and its integrable semi-discrete analogue
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DOI：
10.1088/1751-8121/50/5/055201
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发表时间：
2016-09
期刊：
影响因子：
--
通讯作者：
B. Feng;K. Maruno;Y. Ohta
中科院分区：
文献类型：
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作者：
B. Feng;K. Maruno;Y. Ohta
在本文中，我们提出了一个两个组件的推广约化Ostrovsky（Vakhnenko）方程，其微分形式可以看作是一个两个组件的Degasperis-Procesi（DP）方程的短波极限。由于Lax对的存在，它们是可积的。此外，我们已经表明，两个组件减少Ostrovsky方程可以减少从一个扩展的BKP层次与负流通过伪3-约化和速端图（倒数）变换。作为副产品，它的双线性形式和N-孤子解的pf的形式。一个和两个孤子的解决方案提供和分析。在本文的第二部分，我们从一个改进的BKP方程族出发，它是上述推广的BKP方程族的一个Bäcklund变换，通过定义一个适当的离散速端图变换和因变量变换，构造了一个两分量约化Ostrovsky方程的可积半离散模拟.特别地，上述半离散两分量约化Ostrovsky方程的向后差分形式导致两分量DP方程的短波极限的可积半离散化。给出了它们的N孤子解。
In the present paper, we propose a two-component generalization of the reduced Ostrovsky (Vakhnenko) equation, whose differential form can be viewed as the short-wave limit of a two-component Degasperis–Procesi (DP) equation. They are integrable due to the existence of Lax pairs. Moreover, we have shown that the two-component reduced Ostrovsky equation can be reduced from an extended BKP hierarchy with negative flow through a pseudo 3-reduction and a hodograph (reciprocal) transform. As a by-product, its bilinear form and N-soliton solution in terms of pfaffians are presented. One- and two-soliton solutions are provided and analyzed. In the second part of the paper, we start with a modified BKP hierarchy, which is a Bäcklund transformation of the above extended BKP hierarchy, an integrable semi-discrete analogue of the two-component reduced Ostrovsky equation is constructed by defining an appropriate discrete hodograph transform and dependent variable transformations. In particular, the backward difference form of above semi-discrete two-component reduced Ostrovsky equation gives rise to the integrable semi-discretization of the short wave limit of a two-component DP equation. Their N-soliton solutions in terms of pffafians are also provided.