On the Cauchy Problem for the Periodic Camassa–Holm Equation
1997; Elsevier BV; Volume: 141; Issue: 2 Linguagem: Inglês
10.1006/jdeq.1997.3333
ISSN1090-2732
Autores Tópico(s)Nonlinear Photonic Systems
Resumoand this is the form of the equation with which we are going to work. For more than 15 years, Eq. (1) was known, being derived by Fuchssteiner and Fokas, cf. [8, 9], as a bi-Hamiltonian generalization of the Korteweg-de Vries equation. Actually, in the Fuchssteiner-Fokas derivation there is a computational error: going through it again, one comes up with the exact form of (1), see [10]. As noted in [15], the novelty of Camassa and Holm's work was that they gave a physical derivation of Eq. (1) and found that the solitary waves interact like solitons. The existence of solitons and various other types of special solutions to Eq. (1) is studied extensively (see [1, 2, 7]). For related problems we also refer to [11, 14] and the citations therein. We are interested in the periodic problem for (1), that is, we look for solutions of (1) which are spatially of period 1. We will prove a local article no. DE973333
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