Author(s): Zhijun Qiao
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In this paper, we propose a new completely integrable wave equation: mt+mx(u2−u2x)+2m2ux=0 , m=u−uxx . 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−∣x−ct∣ 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.
This article was published in J. Math. Phys.
and referenced in Journal of Generalized Lie Theory and Applications