He introduced a class of operators of transformation, which is the basis for solving the inverse scattering problem.
12.
The inverse scattering method has had an astonishing variety of generalizations and applications in different areas of mathematics and physics.
13.
It can be solved exactly by use of the inverse scattering transform, as shown by ( see below ).
14.
Tonks Girardeau gas coincide with quantum Nonlinear Schr�dinger equation for infinite repulsion, which can be efficiently analyzed by Quantum inverse scattering method.
15.
The soliton solutions are typically obtained by means of the inverse scattering transform and owe their stability to the integrability of the field equations.
16.
Soon after GGKM, Peter Lax famously interpreted the inverse scattering method in terms of isospectral deformations and so-called " Lax pairs ".
17.
He introduced one of the approaches to the inverse scattering problem for Sturm Liouville operators, and derived what is now called the Marchenko equation.
18.
The authors also constructed a hierarchy of evolution equations integrable via the inverse scattering transform for the 2-dimensional Schr�dinger equation at fixed energy.
19.
By the mid eighty's the initial value problem of integrable evolution equations in one and two space variables was solved via the so called inverse scattering transform.
20.
This was the inverse scattering method, a surprising and elegant method that demonstrates that the KdV equation admits an infinite number of Poisson-commuting conserved quantities and is completely integrable.
