2014/07/29 by Luis Cortés Vega, L. Cortés Vega, A. Restuccia +4 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #hep-th #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.48550/arxiv.1407.7743
In this second version of 23 pages we also considered static solutions which play the role of a background for the system. We also discussed about the regularity of the solutions. We added some figures illustrating the solutions, including the one solitonic solution interacting with the static-background one. We modify the abstract and conclusions in view of these improvements
openalex publication_date 2014/07/29 · arxiv created 2015/01/13 · arxiv updated 2015/01/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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 ε- 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.