title: A new two-component integrable system with peakon solutions.
abstract: A new two-component system with cubic nonlinearity and linear dispersion: [Formula: see text]wherebis an arbitrary real constant, is proposed in this paper. This system is shown integrable with its Lax pair, bi-Hamiltonian structure and infinitely many conservation laws. Geometrically, this system describes a non-trivial one-parameter family of pseudo-spherical surfaces. In the caseb=0, the peaked soliton (peakon) and multi-peakon solutions to this two-component system are derived. In particular, the two-peakon dynamical system is explicitly solved and their interactions are investigated in details. Moreover, a new integrable cubic nonlinear equation with linear dispersion [Formula: see text]is obtained by imposing the complex conjugate reductionv=u* to the two-component system. The complex-valuedN-peakon solution and kink wave solution to this complex equation are also derived.
authors: School of Mathematics and Statistics , Jiangsu Normal University , Xuzhou, Jiangsu 221116, People's Republic of China.
authors: Baoqiang
authors: B
authors: Xia
authors: Department of Mathematics , University of Texas-Pan American , Edinburg TX 78541, USA.
authors: Zhijun
authors: Z
authors: Qiao
keywords: Lax pair; integrable system; peakon