Matrix Boussinesq solitons and their tropical limit
Aristophanes Dimakis, Folkert M\"uller-Hoissen, Xiao-Min Chen
TL;DR
This paper investigates matrix Boussinesq soliton solutions generated through binary Darboux transformations, analyzing their tropical limit to reveal particle-like interactions similar to those observed in KP equation solitons.
Contribution
It introduces a novel analysis of matrix Boussinesq solitons using tropical limits, connecting wave solutions with particle interaction models.
Findings
Tropical limit reveals particle interaction structure of solitons.
Binary Darboux transformation effectively generates matrix Boussinesq solutions.
Connection established between Boussinesq solitons and KP equation tropical behavior.
Abstract
We study soliton solutions of matrix "good" Boussinesq equations, generated via a binary Darboux transformation. Essential features of these solutions are revealed via their "tropical limit", as exploited in previous work about the KP equation. This limit associates a point particle interaction picture with a soliton (wave) solution.
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