Document Type

Article

Publication Date

11-17-2006

Abstract

In this paper, we propose a new completely integrable wave equation: mt+mx u2 −ux 2 +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− −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.

Comments

© 2006, American Institute of Physics. Original published version available at https://doi.org/10.1063/1.2365758

Publication Title

Journal of Mathematical Physics

DOI

10.1063/1.2365758

Included in

Mathematics Commons

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