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The paper studies inverse problems of determining unknown coefficients in various semi-linear and quasi-linear wave equations. We introduce a method to solve inverse problems for non-linear equations using interaction of three waves, that…
The inverse scattering problem for Sturm-Liouville operators on the line with a matrix transfer condition at the origin is considered. We show that the transfer matrix can be reconstructed from the eigenvalues and reflection coefficient. In…
The fractional calculus framework will be used to invert the potential energy function from the classical scattering angle, which will be related to Riemann-Liouville fractional integral. Numerical solution of this fractional order problem…
The inverse scattering method within the $J$-matrix approach to the two coupled-channel problem is discussed. We propose a generalization of the procedure to the case with different thresholds.
In this paper we have chosen to work with two different approaches to solving the inverse problem of the calculus of variation. The first approach is based on an integral representation of the Lagrangian function that uses the first…
We consider a time-dependent linear diffusion equation together with a related inverse boundary value problem. The aim of the inverse problem is to determine, based on observations on the boundary, the non-homogeneous diffusion coefficient…
We propose a scheme for imaging periodic surfaces using a superlens. By employing an inverse scattering model and the transformed field expansion method, we derive an approximate reconstruction formula for the surface profile, assuming…
This is Part II of the paper series on data-compatible T-matrix completion (DCTMC), which is a method for solving nonlinear inverse problems. Part I of the series contains theory and here we present simulations for inverse scattering of…
This article presents a new approach to the real-time solution of inverse problems on embedded systems. The class of problems addressed corresponds to ordinary differential equations (ODEs) with generalized linear constraints, whereby the…
We consider an inverse source problem for partially coherent light propagating in the Fresnel regime. The data is the coherence of the field measured away from the source. The reconstruction is based on a minimum residue formulation, which…
The paper introduces a method to solve inverse problems for hyperbolic systems where the leading order terms are non-linear. We apply the method to the coupled Einstein-scalar field equations and study the question whether the structure of…
We study a multidimensional inverse scattering problem under the time-dependent repulsive Hamiltonians of quadratic type. The time-dependent coefficient on the repulsive term decays as the inverse square of time, which is the threshold…
This paper addresses the challenging and interesting inverse problem of reconstructing the spatially varying dielectric constant of a medium from phaseless backscattering measurements generated by single-point illumination. The underlying…
We consider the wave scattering and inverse scattering in an inhomogeneous medium embedded a homogeneous droplet with a small size, which is modeled by a constant mass density and a small bulk modulus. Based on the Lippmann-Schwinger…
In this work, we propose an observation system based on the available data which solution is one-be-one mapping to the forward problem(with the unknown initial function) solution. It implies their solutions share the same linear structure…
A simple algorithm for the inverse scattering approach to the Camassa-Holm equation is presented.
This work is concerned with an inverse problem of identifying the current source distribution of the time-harmonic Maxwell's equations from multi-frequency measurements. Motivated by the Fourier method for the scalar Helmholtz equation and…
We solve the Cauchy problem of the Ward model in light-cone coordinates using the inverse spectral (scattering) method. In particular we show that the solution can be constructed by solving a $2\times 2$ local matrix Riemann-Hilbert problem…
A variety of inverse Sturm-Liouville problems is considered, including the two-spectrum inverse problem, the problem of recovering the potential from the Weyl function, as well as the recovery from the spectral function. In all cases the…
In this work we study the increasing resolution of linear inverse scattering problems at a large fixed frequency. We consider the problem of recovering the density of a Herglotz wave function, and the linearized inverse scattering problem…