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

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

2008-11-25

arxiv.org/abs/0811.4016v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

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

Scientific paper

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 $u_2$ and the previously known solutions $u_2^{\prime}$ generated from zero seed is given. We present several explicit formulas of the single-soliton solutions for $u_2$ and $u_2^{\prime}$, 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.

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