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arXiv · 2301.07875

Increasing stability of a linearized inverse boundary value problem for a nonlinear Schr\"odinger equation on transversally anisotropic manifolds

Shuai Lu·Jian Zhai
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Abstract

We consider the problem of recovering a nonlinear potential function in a nonlinear Schr\"odinger equation on transversally anisotropic manifolds from the linearized Dirichlet-to-Neumann map at a large wavenumber. By calibrating the complex geometric optics (CGO) solutions according to the wavenumber, we prove the increasing stability of recovering the coefficient of a cubic term as the wavenumber becomes large.

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Shuai Lu, Jian Zhai. 2023-01-19. Increasing stability of a linearized inverse boundary value problem for a nonlinear Schr\"odinger equation on transversally anisotropic manifolds. https://arxiv.org/abs/2301.07875

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