Duality family of KdV equation
Xin Gu, Yuan-Yuan Liu, Wen-Du Li, and Wu-Sheng Dai
TL;DR
This paper uncovers duality families within the KdV equation, linking an infinite set of generalized KdV equations through transformations that allow solutions of one to generate solutions of others.
Contribution
It introduces the concept of duality families for the KdV equation, providing a systematic way to relate and solve multiple generalized KdV equations via duality transformations.
Findings
Existence of duality families in KdV equations
Duality transformations relate solutions across family members
Examples include soliton and periodic solution dualities
Abstract
It is revealed that there exist duality families of the KdV type equation. A duality family consists of an infinite number of generalized KdV (GKdV) equations. A duality transformation relates the GKdV equations in a duality family. Once a family member is solved, the duality transformation presents the solutions of all other family members. We show some dualities as examples, such as the soliton solution-soliton solution duality and the periodic solution-soliton solution duality.
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Taxonomy
TopicsNonlinear Waves and Solitons · Nonlinear Photonic Systems · Numerical methods for differential equations