An Integrable Two‐Component Degasperis–Procesi Equation

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.