Prolongation Structure of a Development Equation and Its Darboux Transformation Solution

Lixiu Wang, Jihong Wang and Yangjie Jia ()
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Lixiu Wang: School of Mathematics and Statistics, Qinghai Normal University, Xining 810008, China
Jihong Wang: School of Mathematics and Statistics, Qinghai Normal University, Xining 810008, China
Yangjie Jia: School of Mathematics and Statistics, Qinghai Normal University, Xining 810008, China

Mathematics, 2025, vol. 13, issue 6, 1-15

Abstract: This paper explores the third-order nonlinear coupled KdV equation utilizing prolongation structure theory and gauge transformation. By applying the prolongation structure method, we obtained an extended version of the equation. Starting from the Lax pairs of the equation, we successfully derived the corresponding Darboux transformation and Bäcklund transformation for this equation, which are fundamental to our solving process. Subsequently, we constructed and calculated the recursive operator for this equation, providing an effective approach to tackling complex problems within this domain. These results are crucial for advancing our understanding of the underlying principles of soliton theory and their implications on related natural phenomena. Our findings not only enrich the theoretical framework but also offer practical tools for further research in nonlinear wave dynamics.

Keywords: recursive operator; Bäcklund transformation; Darboux transformation; Lax pair; prolongation structure (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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