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On the dynamics of Soliton interactions for the Korteweg-de Vries equation

✍ Scribed by A.C. Bryan; A.E.G. Stuart

Publisher
Elsevier Science
Year
1992
Tongue
English
Weight
366 KB
Volume
2
Category
Article
ISSN
0960-0779

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✦ Synopsis

We present a description of the interactions between the individual solitons of a multisoliton solution of the Korteweg-de Vries equation. This analysis is based on an explicit decomposition of the multisoliton into a linear superposition of accelerating solitary waves and interaction terms, thus mimicking the structure of a classical, many-body problem. Our representation, which is distinct from the squared eigenfunction expansion of Gardner et al. [Communs Pure Appl. Math. 27, 97-133 (lY74)] (GGKM), leads to results which are consistent with those obtained by more direct methods. Explicit data are presented for the two-soliton solutions.

πŸ“œ SIMILAR VOLUMES

On the Stochastic Korteweg–de Vries Equa
On the Stochastic Korteweg–de Vries Equation
✍ A de Bouard; A Debussche πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 429 KB

We consider a stochastic Korteweg de Vries equation forced by a random term of white noise type. This can be a model of water waves on a fluid submitted to a random pressure. We prove existence and uniqueness of solutions in H 1 (R) in the case of additive noise and existence of martingales solution