Stable inversion of potential in nonlinear wave equations with cubic nonlinearity

TL;DR

This paper presents a new method for stably recovering potential functions in nonlinear wave equations with cubic nonlinearity, using advanced mathematical tools to improve inversion stability.

Contribution

It introduces a novel approach combining trilinear approximations, symbol estimates, and symbol calculus for stable inversion of lower order coefficients in nonlinear wave equations.

Findings

Established stability estimates for potential inversion

Developed trilinear approximation techniques for nonlinear response

Applied symbol calculus to analyze distorted plane waves

Abstract

This paper investigates inverse potential problems of wave equations with cubic nonlinearity. We develop a methodology for establishing stability estimates for inversion of lower order coefficients. The new ingredients of our approach include trilinear approximations of nonlinear response operators, symbol estimates of distorted plane waves, and lower order symbol calculus.