Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2003-06-03
Nonlinear Sciences
Exactly Solvable and Integrable Systems
18 pages, 16 figures, submitted to JPA; Math. Gen
Scientific paper
10.1088/0305-4470/36/42/008
We describe the interaction pattern in the $x$-$y$ plane for a family of soliton solutions of the Kadomtsev-Petviashvili (KP) equation, $(-4u_{t}+u_{xxx}+6uu_x)_{x}+3u_{yy}=0$. Those solutions also satisfy the finite Toda lattice hierarchy. We determine completely their asymptotic patterns for $y\to \pm\infty$, and we show that all the solutions (except the one-soliton solution) are of {\it resonant} type, consisting of arbitrary numbers of line solitons in both aymptotics; that is, arbitrary $N_-$ incoming solitons for $y\to -\infty$ interact to form arbitrary $N_+$ outgoing solitons for $y\to\infty$. We also discuss the interaction process of those solitons, and show that the resonant interaction creates a {\it web-like} structure having $(N_--1)(N_+-1)$ holes.
Biondini Gino
Kodama Yuji
No associations
LandOfFree
On a family of solutions of the KP equation which also satisfy the Toda lattice hierarchy does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On a family of solutions of the KP equation which also satisfy the Toda lattice hierarchy, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On a family of solutions of the KP equation which also satisfy the Toda lattice hierarchy will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-79064