Uncovers duality in the traveling-wave KdV equation, implying a new method for creating solvable equations.
We reveal a duality in the traveling-wave generalized Korteweg-de Vries (GKdV) equation. Based on this duality, we propose a method for constructing families of exactly solvable equations. Equations related by the duality transformation form a duality family, enabling the derivation of solutions for all members from any single solved equation.
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Gu et al. (2026) studied this question.
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