An integrable semidiscretization of the modified Camassa-Holm equation with linear dispersion term.
An integrable semidiscretization of the modified Camassa-Holm equation with linear dispersion term.
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具有线性色散项的修正 Camassa-Holm 方程的可积半离散化。
DOI：
10.1111/sapm.12497
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Bao-Feng Feng
中科院分区：
文献类型：
--
作者：
Han-Han Sheng;Guo-Fu Yu;Bao-Feng Feng
在本文中，我们对带有线性色散项的修正卡马萨-霍尔姆 (mCH) 方程进行可积离散化。构造的关键是 mCH 方程的一组双线性方程的半离散模拟。首先，我们证明这些双线性方程及其 Gram 型或 Casorati 型行列式解可以通过 Miwa 变换从离散 Kadomtsev-Petviashvili (KP) 方程中简化。然后，通过仔细研究约简过程，我们获得了一组半离散双线性方程及其 Gram 型或 Casorati 型行列式形式的一般孤子解。最后，通过定义因变量和离散速图变换，我们能够导出 mCH 方程的可积半离散模拟。还表明，半离散 mCH 方程在连续统极限下收敛到连续方程。
In the present paper, we are with integrable discretization of a modified Camassa–Holm (mCH) equation with linear dispersion term. The key of the construction is the semidiscrete analog for a set of bilinear equations of the mCH equation. First, we show that these bilinear equations and their determinant solutions either in Gram‐type or Casorati‐type can be reduced from the discrete Kadomtsev–Petviashvili (KP) equation through Miwa transformation. Then, by scrutinizing the reduction process, we obtain a set of semidiscrete bilinear equations and their general soliton solution in Gram‐type or Casorati‐type determinant form. Finally, by defining dependent variables and discrete hodograph transformations, we are able to derive an integrable semidiscrete analog of the mCH equation. It is also shown that the semidiscrete mCH equation converges to the continuous one in the continuum limit.