School of Mathematical and Statistical Sciences Faculty Publications and Presentations

An Integrable Two-Component Degasperis–Procesi Equation

Document Type

Article

Publication Date

3-25-2025

Abstract

We propose a new two-component Degasperis–Procesi (2-DP) equation, which is shown to be integrable. First of all, we derive an integrable three-component system from the Witten–Dijkgraaf–Verlinde–Verlinde (WDVV) associativity equation and construct its Lax pair and bi-Hamiltonian structure. Next, a 2-DP equation is proposed as further reduction of this three-component system, along with its Lax pair and associated bi-Hamiltonian structure. A reciprocal transformation is found to connect the 2-DP equation with a negative flow in a coupled KdV hierarchy, the associated system has the property of Painlevé. Finally, infinitely many conserved quantities, simple periodic and soliton solutions for the newly integrable 2-DP equation are provided.

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https://onlinelibrary.wiley.com/share/C4HAIGVMFHKI3QX4HM2P?target=10.1111/sapm.70045

Publication Title

Studies in Applied Mathematics

DOI

10.1111/sapm.70045

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