An integrable equation with nonsmooth solitons
An integrable equation with nonsmooth solitons
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DOI：
10.1007/s11232-011-0044-8
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发表时间：
2011-06
影响因子：
1
通讯作者：
Z. Qiao;Xianqi Li
中科院分区：
文献类型：
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作者：
Z. Qiao;Xianqi Li
给出了方程ρt= bux+（1/2）[（u2− ux 2）ρ]x的双Hamilton结构和Lax对，其中ρ = u − uxx，B =const，保证了它在Lax对意义下的可积性.研究了该方程的非光滑孤子解，证明了在空间和时间无穷远处，当边界条件u → 0为零时，该方程既有“W/M”型的尖峰孤子解，又有尖点孤子解.
We present the bi-Hamiltonian structure and Lax pair of the equation ρt= bux+(1/2)[(u2−ux2)ρ]x, where ρ = u − uxxand b =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 →0at the space and time infinities, the equation has both “W/M-shape” peaked soliton (peakon) and cusped soliton (cuspon) solutions.