42 research outputs found

### Bose-Einstein condensates with F=1 and F=2. Reductions and soliton interactions of multi-component NLS models

We analyze a class of multicomponent nonlinear Schrodinger equations (MNLS)
related to the symmetric BD.I-type symmetric spaces and their reductions. We
briefly outline the direct and the inverse scattering method for the relevant
Lax operators and the soliton solutions. We use the Zakharov-Shabat dressing
method to obtain the two-soliton solution and analyze the soliton interactions
of the MNLS equations and some of their reductions.Comment: SPIE UNO-09-UN101-19, SPIE Volume: 7501, (2009

### Rational Bundles and Recursion Operators for Integrable Equations on A.III-type Symmetric Spaces

We analyze and compare the methods of construction of the recursion operators
for a special class of integrable nonlinear differential equations related to
A.III-type symmetric spaces in Cartan's classification and having additional
reductions.Comment: 13 pages, 1 figur

### Reductions of integrable equations on A.III-type symmetric spaces

We study a class of integrable non-linear differential equations related to
the A.III-type symmetric spaces. These spaces are realized as factor groups of
the form SU(N)/S(U(N-k) x U(k)). We use the Cartan involution corresponding to
this symmetric space as an element of the reduction group and restrict generic
Lax operators to this symmetric space. The symmetries of the Lax operator are
inherited by the fundamental analytic solutions and give a characterization of
the corresponding Riemann-Hilbert data.Comment: 14 pages, 1 figure, LaTeX iopart styl

### Black Sea coastal forecasting system

The Black Sea coastal nowcasting and forecasting system was built within the framework of EU FP6 ECOOP (European COastalshelf sea OPerational observing and forecasting system) project for five regions: the south-western basin along the coasts of Bulgaria and Turkey, the north-western shelf along the Romanian and Ukrainian coasts, coastal zone around of the Crimea peninsula, the north-eastern Russian coastal zone and the coastal zone of Georgia. The system operates in the real-time mode during the ECOOP project and afterwards. The forecasts include temperature, salinity and current velocity fields. Ecosystem model operates in the off-line mode near the Crimea coast

### On the (Non)-Integrability of KdV Hierarchy with Self-consistent Sources

Non-holonomic deformations of integrable equations of the KdV hierarchy are
studied by using the expansions over the so-called "squared solutions" (squared
eigenfunctions). Such deformations are equivalent to perturbed models with
external (self-consistent) sources. In this regard, the KdV6 equation is viewed
as a special perturbation of KdV equation. Applying expansions over the
symplectic basis of squared eigenfunctions, the integrability properties of the
KdV hierarchy with generic self-consistent sources are analyzed. This allows
one to formulate a set of conditions on the perturbation terms that preserve
the integrability. The perturbation corrections to the scattering data and to
the corresponding action-angle variables are studied. The analysis shows that
although many nontrivial solutions of KdV equations with generic
self-consistent sources can be obtained by the Inverse Scattering Transform
(IST), there are solutions that, in principle, can not be obtained via IST.
Examples are considered showing the complete integrability of KdV6 with
perturbations that preserve the eigenvalues time-independent. In another type
of examples the soliton solutions of the perturbed equations are presented
where the perturbed eigenvalue depends explicitly on time. Such equations,
however in general, are not completely integrable.Comment: 16 pages, no figures, LaTe

### Nonlocal Reductions of the Ablowitzâ€“Ladik Equation

Our purpose is to develop the inverse scattering transform for the nonlocal semidiscrete nonlinear SchrĂ¶dinger equation (called the Ablowitzâ€“Ladik equation) with PT symmetry. This includes the eigenfunctions (Jost solutions) of the associated Lax pair, the scattering data, and the fundamental analytic solutions. In addition, we study the spectral properties of the associated discrete Lax operator. Based on the formulated (additive) Riemannâ€“Hilbert problem, we derive the one- and two-soliton solutions for the nonlocal Ablowitzâ€“Ladik equation. Finally, we prove the completeness relation for the associated Jost solutions. Based on this, we derive the expansion formula over the complete set of Jost solutions. This allows interpreting the inverse scattering transform as a generalized Fourier transform