Abstract
We present the bi-Hamiltonian structure and Lax pair of the equation ρt = bux+(1/2)[(u2−u 2x )ρ]x, where ρ = u − uxx and 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 → 0 at the space and time infinities, the equation has both “W/M-shape” peaked soliton (peakon) and cusped soliton (cuspon) solutions.
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Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 167, No. 2, pp. 214–221, May, 2011.
An erratum to this article can be found at http://dx.doi.org/10.1007/s11232-011-0128-5
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Qiao, Z., Li, X. An integrable equation with nonsmooth solitons. Theor Math Phys 167, 584–589 (2011). https://doi.org/10.1007/s11232-011-0044-8
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DOI: https://doi.org/10.1007/s11232-011-0044-8