English

Solutions of the (2+1)-dimensional KP, SK and KK equations generated by gauge transformations from non-zero seeds

Exactly Solvable and Integrable Systems 2015-05-13 v1

Abstract

By using gauge transformations, we manage to obtain new solutions of (2+1)-dimensional Kadomtsev-Petviashvili(KP), Kaup-Kuperschmidt(KK) and Sawada-Kotera(SK) equations from non-zero seeds. For each of the preceding equations, a Galilean type transformation between these solutions u2u_2 and the previously known solutions u2u_2^{\prime} generated from zero seed is given. We present several explicit formulas of the single-soliton solutions for u2u_2 and u2u_2^{\prime}, and further point out the two main differences of them under the same value of parameters, i.e., height and location of peak line, which are demonstrated visibly in three figures.

Keywords

Cite

@article{arxiv.0811.4016,
  title  = {Solutions of the (2+1)-dimensional KP, SK and KK equations generated by gauge transformations from non-zero seeds},
  author = {Jingsong He and Xiaodong Li},
  journal= {arXiv preprint arXiv:0811.4016},
  year   = {2015}
}

Comments

18 pages, 6 figures, to appear in Journal of Nonlinear Mathematical Physics