Geodesic
An integrable equation with nonsmooth solitons
Teoretičeskaâ i matematičeskaâ fizika, Tome 167 (2011) no. 2, pp. 214-221 Cet article a éte moissonné depuis la source Math-Net.Ru

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We present the bi-Hamiltonian structure and Lax pair of the equation $\rho_t= bu_x+(1/2)[(u^2-u_x^2)\rho]_x$, where $\rho=u-u_{xx}$ and $b=\mathrm{const}$, which guarantees its integrability in the Lax pair sense. We study nonsmooth soliton solutions of this equation and show that under the vanishing boundary condition $u\to0$ at the space and time infinities, the equation has both “W/M-shape” peaked soliton (peakon) and cusped soliton (cuspon) solutions.
Keywords: integrable equation, peakon, cuspon.
Mots-clés : Lax pair 
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Zhijun Qiao; Xianqi Li. An integrable equation with nonsmooth solitons. Teoretičeskaâ i matematičeskaâ fizika, Tome 167 (2011) no. 2, pp. 214-221. http://geodesic.mathdoc.fr/item/TMF_2011_167_2_a4/

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