Modulational stability of ground states to nonlinear Kirchhoff equations
Jianjun Zhang, Zhisu Liu, Marco Squassina
TL;DR
This paper analyzes the stability of ground states in a nonlinear Schrödinger equation with Kirchhoff term, providing spectral analysis and modulation stability estimates to understand their robustness.
Contribution
It introduces a spectral analysis approach to establish modulation stability of ground states in Kirchhoff-type nonlinear Schrödinger equations, extending previous stability results.
Findings
Spectral analysis of the linearized operator
Modulation stability estimate for ground states
Extension of Weinstein's stability framework
Abstract
We investigate the stability of ground states to a nonlinear focusing Schr\"odinger equation in presence of a Kirchhoff term. Through a spectral analysis of the linearized operator about ground states, we show a modulation stability estimate of ground states in the spirit of one due to Weinstein [{\it SIAM J. Math. Anal.}, 16(1985),472-491].
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Nonlinear Photonic Systems · Mathematical Analysis and Transform Methods