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arXiv · 1407.7743

Multisolitonic solutions from a Bäcklund transformation for a parametric coupled Korteweg-de Vries system

L. Cortés Vega·A. Restuccia·A. Sotomayor
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Abstract

We introduce a parametric coupled KdV system which contains, for particular values of the parameter, the complex extension of the KdV equation and one of the Hirota-Satsuma integrable systems. We obtain a generalized Gardner transformation and from the associated $\varepsilon$- deformed system we get the infinite sequence of conserved quantities for the parametric coupled system. We also obtain a Bäcklund transformation for the system. We prove the associated permutability theorem corresponding to such transformation and we generate new multi-solitonic and periodic solutions for the system depending on several parameters. We show that for a wide range of the parameters the solutions obtained from the permutability theorem are regular solutions. Finally we found new multisolitonic solutions propagating on a non-trivial regular static background.

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L. Cortés Vega, A. Restuccia, A. Sotomayor. 2015-01-13. Multisolitonic solutions from a Bäcklund transformation for a parametric coupled Korteweg-de Vries system. https://arxiv.org/abs/1407.7743

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