Multisoliton solutions of 3,4,6 waves problems connectet with semisimlealgebras of the second rank $A_3,B_2=C_2,G_2$

TL;DR

This paper derives explicit multisoliton solutions for wave interaction systems linked to second-rank semisimple algebras, enhancing understanding of algebraic structures in nonlinear wave phenomena.

Contribution

It provides explicit multisoliton solutions for wave interaction problems associated with second-rank semisimple algebras, a novel connection in this field.

Findings

Explicit multisoliton solutions for A3, B2, C2, G2 algebras

Connection between wave systems and algebraic structures

Enhanced understanding of wave interactions in algebraic context

Abstract

With each semisimple algebra it is possible to connect the system of interacting waves. The number of interacting fields coincides with the number of positive roots of corresponding semisimple algebra. Multisoliton solution of such kind problem are represented in explicit form for the algebras of second rank.