Width of the analyticity strip in space variable of viscous Burgers shockwaves

TL;DR

This paper investigates the analyticity properties of viscous shock solutions in the generalized Burgers equation, showing that perturbed waves regain their analyticity within a specific strip in the complex plane.

Contribution

It provides a detailed analysis of the analyticity strip width for viscous Burgers shockwaves, extending understanding of their complex-analytic structure.

Findings

Perturbed shockwaves recover analyticity in a finite strip.

The width of the analyticity strip is determined by the first singularities.

Analytic continuation properties depend on the nature of the nonlinear source term.

Abstract

Analytic continuation of viscous shock solution for the generalized Burgers equation with polynomial nonlinear source term is investigated. We show that a pertubated wave recovers its analyticity in the space variable in the strip limited by the first pair of singularities of the wave.