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<p>Both the Darboux transformation (DT) and Bäcklund transformation (BT) approaches of the modified Camassa-Holm (mCH) equation are restudied. The <i>N</i>-DT is constructed for the mCH equation in a simple and direct way. By extending the existing 1-BT and 2-BT, the <i>N</i>-BT of the mCH equation is obtained. It is argued that two multi-soliton solution formulae resulted from <i>N</i>-DT and <i>N</i>-BT are equivalent. Furthermore, the DT method is applied to calulate some explicit solutions which include a solution expressed in terms of trigonometric functions.</p>

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Darboux and Bäcklund transformations approaches of the modified Camassa-Holm equation

  • 期刊论文

  • 发表日期：

    2025年7月18日

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  • Xiaoxing Niu,
  • Q. P. Liu,
  • Nianhua Li

摘要

Both the Darboux transformation (DT) and Bäcklund transformation (BT) approaches of the modified Camassa-Holm (mCH) equation are restudied. The N-DT is constructed for the mCH equation in a simple and direct way. By extending the existing 1-BT and 2-BT, the N-BT of the mCH equation is obtained. It is argued that two multi-soliton solution formulae resulted from N-DT and N-BT are equivalent. Furthermore, the DT method is applied to calulate some explicit solutions which include a solution expressed in terms of trigonometric functions.