Related papers: Complete Integrability of Completely Integrable Sy…
A classical (or quantum) superintegrable system on an n-dimensional Riemannian manifold is an integrable Hamiltonian system with potential that admits 2n-1 functionally independent constants of the motion that are polynomial in the momenta,…
We show that the motion on the n-dimensional ellipsoid is complete integrable by exhibiting n integrals in involution. The system is separable at classical and quantum level, the separation of classical variables being realized by the…
This paper presents high-order integral equation methods for evaluation of electromagnetic wave scattering by dielectric bumps and dielectric cavities on perfectly conducting or dielectric half-planes. In detail, the algorithms introduced…
A cylindrical wave expansion method is developed to obtain the scattering field for an ideal two-dimensional cylindrical invisibility cloak. A near-ideal model of the invisibility cloak is set up to solve the boundary problem at the inner…
In this contribution we describe the role of several two-component integrable systems in the classical problem of shallow water waves. The starting point in our derivation is the Euler equation for an incompressible fluid, the equation of…
Achieving exact unidirectional invisibility in a finite frequency band has been an outstanding problem for many years. We offer a simple solution to this problem in two dimensions that is based on our solution to another more basic open…
We present a solution method for the integrable system (derivative nonlinear Schr\"odinger II system) or the Chen--Lee--Liu system. This is done by presenting a solution technique for the inverse scattering problem for the corresponding…
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…
We consider the one-dimensional nonlinear Schr\"odinger equation with a nonlinearity of degree $p>1$. We exhibit measures on the space of initial data for which we describe the non trivial evolution by the linear Schr\"odinger flow and we…
The main objective of this work is to investigate the integrability and linearizability problems around a singular point at the origin of the family of differential systems Particularly we are interested in the three-dimensional cubic…
The formalism of quantum systems with diagonal singularities is applied to describe scattering processes. Well defined states are obtained for infinite time, which are related to a ''weak form'' of intrinsic irreversibility. Real and…
We derive a fully discrete Inverse Scattering Transform as a method for solving the initial-value problem for the Q3$_\delta$ lattice (difference-difference) equation for real-valued solutions. The initial condition is given on an infinite…
In this paper we show that if one writes down the structure equations for the evolution of a curve embedded in an (n)-dimensional Riemannian manifold with constant curvature this leads to a symplectic, a Hamiltonian and an hereditary…
To analyse pure ${\cal N}=2$ $SU(2)$ gauge theory in the Nekrasov-Shatashvili (NS) limit (or deformed Seiberg-Witten (SW)), we use the Ordinary Differential Equation/Integrable Model (ODE/IM) correspondence, and in particular its (broken)…
We consider the inverse resonance problem in one-dimensional scattering theory. The scattering matrix consists of $2\times 2$ entries of meromorphic functions, which are quotients of certain Fourier transform. The resonances are expressed…
In this note the notion of infinitesimal scattering matrix is introduced. It is shown that under certain assumption, the scattering operator of a pair of trace compatible operators is equal to the chronological exponential of the…
Particle production in integrable field theories may exist depending on the vacuum around which excitations are defined. To tackle this and analogous issues with conventional field theoretical tools, we consider the integrable…
In analogy with the well-known 2-linkage tractor-trailer problem, we define a 2-linkage problem in the plane with novel non-holonomic ``no-slip'' conditions. Using constructs from sub-Riemannian geometry, we look for geodesics corresponding…
We consider evolution equations for curves in the 3-dimensional sphere $S^3$ that are invariant under the group $SU(2,1)$ of pseudoconformal transformations, which preserves the standard contact structure on the sphere. In particular, we…
Lotka-Volterra model is one of the most popular in biochemistry. It is used to analyze cooperativity, autocatalysis, synchronization at large scale and especially oscillatory behavior in biomolecular interactions. These phenomena are in…