We survey mathematical developments in the inverse method of electrical impedance
tomography which consists in determining the electrical properties of a medium by making …

This survey article deals mainly with two inverse problems and the relation between them.
The first inverse problem we consider is whether one can determine the electrical …

We show that the coefficient γ (x) of the elliptic equation∇·(γ∇ u)= 0 in a two-dimensional
domain is uniquely determined by the corresponding Dirichlet-to-Neumann map on the …

The most well-known methods for the exact analysis of boundary value problems for linear
PDEs are the methods of (a) classical transforms,(b) images, and (c) Green's function …

By using the solutions of an auxiliary ordinary differential equation, a direct algebraic
method is described to construct several kinds of exact travelling wave solutions for some …

A generalisation in 2+ 1 dimensions of the Korteweg-de Vries equation is related to the
spectral problem (delta x 2-delta y 2-p (x, y)) phi (x, y; k)= 0. It can contain arbitrary functions …

Localized (exponentially decaying in all directions) soliton solutions of the evolution
equations related to the Zakharov-Shabat spectral problem in the plane are explicitly given …

In this paper, we present a systematical inverse scattering transform for both focusing and
defocusing nonlocal (reverse-space–time) modified Korteweg–de Vries (mKdV) equations …

The book is devoted to the mathematical theory of soliton phenomena on the plane. The
inverse spectral transform method which is a main tool for the study of the (2+ 1) …

Integrable nonlinear evolution equations in one‐spatial and one‐temporal dimensions
possess a remarkably rich algebraic structure: Infinitely many symmetries and conserved …