Multisolitonic solutions from a B'acklund transformation for a parametric coupled Korteweg-de Vries system

摘要

We introduce a parametric coupled KdV system which contains, for particularvalues of the parameter, the complex extension of the KdV equation and one ofthe Hirota-Satsuma integrable systems. We obtain a generalized Gardnertransformation and from the associated $\varepsilon$- deformed system we getthe infinite sequence of conserved quantities for the parametric coupledsystem. We also obtain a B\"{a}cklund transformation for the system. We provethe associated permutability theorem corresponding to such transformation andwe generate new multi-solitonic and periodic solutions for the system dependingon several parameters. We show that for a wide range of the parameters thesolutions obtained from the permutability theorem are regular solutions.Finally we found new multisolitonic solutions propagating on a non-trivialregular static background.