A three-component generalization of Camassa–Holm equation with N-peakon solutions

By Xianguo Geng, Bo Xue. 2011

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Abstract A three-component generalization of Camassa–Holm equation with peakon solutions is proposed, which is associated with a 3 × 3 matrix spectral problem with three potentials. With the aid of the zero-curvature equation, we derive a hierarchy of new nonlinear evolution equations and establish their Hamiltonian structures. The three-component generalization of Camassa–Holm equation is exactly a negative flow in the hierarchy and admits exact solutions with N -peakons and an infinite sequence of conserved quantities.

Subfields: Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/689c4d319bcb3466f0eb05b14c4c447bb655280a