Multisolitonic solutions from a B\"acklund transformation for a   parametric coupled Korteweg-de Vries system
  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 B\"{a}cklund 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. 
L. Cort\'es Vega, A. Restuccia and A. Sotomayor
math-ph hep-th math.MP nlin.SI