Existence and asymptotic behavior of Padé approximants to the Korteweg–de-Vries multisoliton solutions
- 1 January 1983
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 24 (1) , 53-64
- https://doi.org/10.1063/1.525602
Abstract
The summation procedure of the Padé type is applied to the perturbation expansion of the solution of the potential Korteweg-de-Vries equation (K.d.V.), introduced by Rosales. For the N-soliton solution without background the [(n−1)/n] Padé approximants are shown to exist for n≤N. Their asymptotic behavior is investigated and it is found that it corresponds to a system of n solitons with the leading velocity parameters. The analogous results for the K.d.V. then follow in agreement with some previous numerical observations.Keywords
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