A new integrable equation with peakon solutions

被引：682

作者：

Degasperis, A ^{[1
]}

Holm, DD

Hone, ANW

机构：

[1] Univ Roma La Sapienza, Dipartimento Fis, Sez Roma, Ist Nazl Fis Nucl, Rome, Italy

[2] Los Alamos Natl Lab, Div Theoret, Los Alamos, NM USA

[3] Los Alamos Natl Lab, Ctr Nonlinear Studies, Los Alamos, NM 87545 USA

[4] Univ Kent, Inst Math & Stat, Canterbury, Kent, England

来源：

THEORETICAL AND MATHEMATICAL PHYSICS | 2002年 / 133卷 / 02期

关键词：

peakons; reciprocal transformations; weak solutions;

D O I：

10.1023/A:1021186408422

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We consider a new partial differential equation recently obtained by Degasperis and Procesi using the method of asymptotic integrability; this equation has a form similar to the Camassa-Holm shallow water wave equation. We prove the exact integrability of the new equation by constructing its Lax pair and explain its relation to a negative flow in the Kaup-Kupershmidt hierarchy via a reciprocal transformation. The infinite sequence of conserved quantities is derived together with a proposed bi-Hamiltonian structure, The equation admits exact solutions as a superposition of multipeakons, and we describe the integrable finite-dimensional peakon dynamics and compare it with the analogous results for Camassa-Holm peakons.

引用

页码：1463 / 1474

页数：12

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