Normal form for transverse instability of gZK equation for the line soliton with nearly critical speed

TL;DR

This paper investigates the transverse instability of line solitons in the generalized Zakharov-Kuznetsov equation near critical speed, deriving a normal form reduction for the bifurcation problem on a product space.

Contribution

It introduces a normal form reduction approach for analyzing bifurcations related to the transverse instability of solitons in the gZK equation.

Findings

Normal form reduction for bifurcation analysis

Insights into the stability near critical speed

Mathematical justification of the reduction process

Abstract

In this paper, we study the transverse instability of generalized Zakharov-Kuznetsov equation for the line soliton with critical speed. We derive and justify a normal form reduction for a bifurcation problem of the stationary nonlinear KdV equation on the product space R ? T.