Starting from the truncated Painlevé expansion, auto- and non-auto Bäcklund transformations are constructed for an extended (2+1)-dimensional Korteweg–de Vries equation. Then nonlocal residual symmetry is derived and localized to obtain the finite group transformation. By virtue of a simple connection between the truncated Painlevé expansion and the consistent tanh expansion (CTE) method, exact single soliton and resonant two-soliton solutions as well as interaction solutions between soliton and cnoidal wave are presented explicitly.

中文翻译：

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扩展 (2+1) 维 Korteweg-de Vries 方程的 Bäcklund 变换、残差对称性和精确相互作用解

从截断的 Painlevé 展开开始，为扩展的 (2+1) 维 Korteweg-de Vries 方程构造自动和非自动 Bäcklund 变换。然后导出非局部残差对称性并进行局部化，得到有限群变换。凭借截断的 Painlevé 展开和一致 tanh 展开 (CTE) 方法之间的简单联系，明确提出了精确的单孤子和共振双孤子解以及孤子和 cnoidal 波之间的相互作用解。