We present the mathematical foundation for a point-source method to solve some inverse acoustic and electromagnetic obstacle scattering problems in three dimensions. We investigate the inverse acoustic scattering problem by a sound-soft and a sound-hard scatterer and the inverse electromagnetic scattering problem by a perfect conductor. Two independent approaches to the method are presented whi...

We show that integrability of the BCS model extends beyond Richardson's model (where all Cooper pair scatterings have equal coupling) to that of the russian doll BCS model for which the couplings have a particular phase dependence that breaks time-reversal symmetry. This model is shown to be integrable using the quantum inverse scattering method, and the exact solution is obtained by means of t...

The author’s method for solving inverse scattering problem with fixed-energy data is described. Its comparison with the method based on the D-N map is given. A new inversion procedure is formulated. c © 2008 Elsevier Ltd. All rights reserved. MSC: 35R30; 47H17; 65M30; 81U05 PACS: 03.80.+r.; 03.65.Nk

Inverse scattering methods capable of compressive imaging are proposed and analyzed. The methods employ randomly and repeatedly (multipleshot) the single-input–single-output (SISO) measurements in which the probe frequencies, the incident, and the sampling directions are related in a precise way and are capable of recovering exactly scatterers of sufficiently low sparsity. For point targets, va...

Formation of fermion bag solitons is an important paradigm in the theory of hadron structure. We report here on our non-perturbative analysis of this phenomenon in the 1+1 dimensional massive Gross-Neveu model, in the large N limit. Our main result is that the extremal static bag configurations are reflectionless, as in the massless Gross-Neveu model. Explicit formulas for the profiles and mass...

If an acoustic field is governed by the equation V 2 u + w 2 u + u2al (x)u + V (az(x)Vu) = -S(x-y) in R and U is measured on the surface of the earth, i.e. on the plane x3 = 0 for all positions of the source y and receiver x and for all frequencies, then: (i) we show that the low frequency portion of the data determines a 2 ( x ) while the high frequency portion of the data determines ( a , -a2...

We formulate in terms of the quantum inverse scattering method the algebraic Bethe ansatz solution of the one-dimensional Hubbard model. The method developed is based on a new set of commutation relations which encodes a hidden symmetry of 6-vertex type.