On asymptotic stability on a center hypersurface at the soliton for even solutions of the NLKG when $2\ge p> \frac{5}{3}$

TL;DR

This paper extends the understanding of asymptotic stability at the soliton for even solutions of the defocusing power Nonlinear Klein-Gordon Equation to a broader range of the nonlinearity parameter p, specifically from p>3 down to 2≥p>5/3.

Contribution

It generalizes previous stability results to include the case where 2≥p>5/3, expanding the known parameter range for asymptotic stability at the soliton.

Findings

Established asymptotic stability on a center hypersurface for 2≥p>5/3.

Extended previous results from p>3 to a wider range including p>5/3.

Confirmed stability properties for even solutions of the NLKG in the specified parameter range.

Abstract

We extend the result M. Kowalczyk, Y. Martel, C. Mu\~noz, JEMS 2022, on the existence, in the context of spatially even solutions, of asymptotic stability on a center hypersurface at the soliton of the defocusing power Nonlinear Klein Gordon Equation with $p>3$, to the case $2\ge p> \frac{5}{3}$.