A new integrable equation with cuspons and W/M-shape-peaks solitons

In this paper, we propose a new completely integrable wave equation: m(t)+m(x)(u(2)-u(x)(2))+2m(2)u(x)=0, m=u-u(xx). The equation is derived from the two dimensional Euler equation and is proven to have Lax pair and bi-Hamiltonian structures. This equation possesses new cusp solitons-cuspons, instead of regular peakons ce(-parallel to x-ct parallel to) with speed c. Through investigating the equation, we develop a new kind of soliton solutions-"W/M"-shape-peaks solitons. There exist no smooth solitons for this integrable water wave equation. (c) 2006 American Institute of Physics.