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

作者：Geng Xianguo^*; Xue Bo

来源：Advances in Mathematics, 2011, 226(1): 827-839.

DOI：10.1016/j.aim.2010.07.009

• Three-component generalization of Camassa-Holm equation
• N-peakon solutions
• Dynamical system
• Infinitely many conservation laws

A three-component generalization of Camassa-Holm equation with peakon solutions is proposed, which is associated with a 3 x 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.

• 出版日期2011-1-15
• 单位郑州大学