相关论文: Multi-Field Integrable Systems Related to WKI-Type…
In the paper we obtain equations for large-scale fluctuations of the mean field (the field of magnetization and quadrupole moments) in a magnetic system realized by a square (cubic) lattice of atoms with spin s >= 1 at each site. We use the…
A systematic construction of St\"{a}ckel systems in separated coordinates and its relation to bi-Hamiltonian formalism are considered. A general form of related hydrodynamic systems, integrable by the Hamilton-Jacobi method, is derived. One…
A classification of integrable two-component systems of non-evolutionary partial differential equations that are analogous to the Camassa-Holm equation is carried out via the perturbative symmetry approach. Independently, a classification…
We present an extension of the previously proposed mean-field renormalization method to model Hamiltonians which are characterized by more than just one type of interaction. The method rests on scaling assumptions about the magnetization of…
We develop a mean-field theory of carrier-induced ferromagnetism in diluted magnetic semiconductors. Our approach represents an improvement over standard RKKY model allowing spatial inhomogeneity of the system, free-carrier spin…
The Lax representation and Backlund transformations for the systems similar to WZNW (Wess-Zumino-Novicov-Witten) systems and non-abelian affine Toda models are obtained in present paper. One of these systems is a new integrable extension of…
We consider the probability to find a string of $x$ adjacent parallel spins in the antiferromagnetic ground state of the model (in a magnetic field). We derive a system of integro-difference equations which define this probability. This…
We construct a point transformation between two integrable systems, the multi-component Harry Dym equation and the multi-component extended Harry Dym equation, that does not preserve the class of multi-phase solutions. As a consequence we…
The ferromagnetic spin exchange interaction between the itinerant electrons and localized moments on a periodic lattice, studied within the so-called Kondo lattice model (KLM), is considered for multiband situation where the hopping…
The generalized Zakharov-Shabat systems with complex-valued non-regular Cartan elements and the systems studied by Caudrey, Beals and Coifman (CBC systems) and their gauge equivalent are studied. This study includes: the properties of…
Starting from a general relativistic kinetic equation, a self-consistent mean-field equation for fermions is derived within a covariant density matrix approach of QED plasmas in strong external fields. A Schr\"odinger picture formulation on…
The Darboux-Dressing Transformations are applied to the Lax pair associated to systems of coupled nonlinear wave equations in the case of boundary values which are appropriate to both bright and dark soliton solutions. The general formalism…
In a recent work, two of the authors have formulated the non-linear space-time Hasegawa-Mima plasma equation as a coupled system of two linear PDEs, a solution of which is a pair $(u,w)$, with $w=(I-\Delta)u$. The first equation is of…
The solutions of the Wigner-transformed time-dependent Hartree--Fock--Bogoliubov equations are studied in the constant-$\Delta$ approximation. This approximation is known to violate particle-number conservation. As a consequence, the…
The higher-order superintegrability of separable potentials is studied. It is proved that these potentials possess (in addition to the two quadratic integrals) a third integral of higher-order in the momenta that can be obtained as the…
We consider dispersionless Lax systems and present a new systematic method of deriving new integrable systems from a given one. We provide examples that include: the dispersionless Hirota equation, the general heavenly equation and the web…
For linear Hamiltonian $2n\times 2n$ systems $J y'(x) = (\lambda W(x)+H(x))y(x)$ we investigate the problem how the eigenvalues $\lambda$ depend on the entries of the coefficient matrix $H$. This question turns into a deformation equation…
By explicitly including fractionally ionic contributions to the polarizability of a many-component system we are able to significantly improve on previous atom-wise many-body van der Waals approaches with essentially no extra numerical…
Hyperbolic versions of the integrable (1+1)-dimensional Heisenberg Ferromagnet and sigma models are discussed in the context of topological solutions classifiable by an integer `winding number'. Some explicit solutions are presented and the…
A class of multi-component integrable systems associated to Novikov algebras, which interpolate between KdV and Camassa-Holm type equations, is obtained. The construction is based on the classification of low-dimensional Novikov algebras by…