In this paper, we propose a new completely integrable wave equation: , . 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 with speed . 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.
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2006
American Institute of Physics
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