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<p>A direct linearisation scheme, based on an elliptic Cauchy kernel, is set up for the lattice CKP equation. This leads to an elliptic parametrisation of the lattice CKP equation, which allows us to perform appropriate continuum limits and construct elliptic solutions. By selecting appropriate integration measures and domains for the singular linear integral equation in the scheme, elliptic multi-soliton solutions of the lattice CKP equation are found. Also a Lax triplet associated with the system is derived from the direct linearisation scheme.</p>

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Elliptic solutions of the lattice CKP equation and its elliptic direct linearisation scheme

  • 期刊论文

  • 发表日期：

    2026年4月17日

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  • Ying-ying Sun,
  • Da-jun Zhang,
  • Frank Nijhoff

摘要

A direct linearisation scheme, based on an elliptic Cauchy kernel, is set up for the lattice CKP equation. This leads to an elliptic parametrisation of the lattice CKP equation, which allows us to perform appropriate continuum limits and construct elliptic solutions. By selecting appropriate integration measures and domains for the singular linear integral equation in the scheme, elliptic multi-soliton solutions of the lattice CKP equation are found. Also a Lax triplet associated with the system is derived from the direct linearisation scheme.