Related papers: Bosonic Super Liouville System: Lax Pair and Solut…
We construct Lax pairs for the recently (2023) introduced integrable PDE systems known as the BKM equations. As many known and previously studied integrable systems are special cases of the BKM systems, our construction provides Lax pairs…
Liouville theorems for scaling invariant nonlinear elliptic systems (saying that the system does not possess nontrivial entire solutions) guarantee a priori estimates of solutions of related, more general systems. Assume that $p=2q+3>1$ is…
A new method is proposed to generate nonlinear integrable systems by starting with existing Lax pair and a new form of Kr\"onecker product. It is observed that such equation can be generated with the help of a Hamiltonian structure.…
We investigate the mechanism of formation of supermixed soliton-like states in bosonic binary mixtures loaded in ring lattices. We evidence the presence of a common pathway which, irrespective of the number of lattice sites and upon…
Supersymmetric extensions of Hamilton-Jacobi separable Liouville mechanical systems with two degrees of freedom are defined. It is shown that supersymmetry can be implemented in this type of systems in two independent ways. The structure of…
Determining whether a dynamical system is integrable is generally a difficult task which is currently done on a case by case basis requiring large human input. Here we propose and test an automated method to search for the existence of…
Small perturbation of the Liouville equation under smooth initial data is considered. Asymptotic solution which is available for a long time interval is constructed by the two scale method.
We propose a mechanism for liquid formation in strongly correlated lattice systems. The mechanism is based on an interplay between long-range attraction and superexchange processes. As an example, we study dipolar bosons in one-dimensional…
The particular case of the integrable two component (2+1)-dimensional hydrodynamical type systems, which generalises the so-called Hamiltonian subcase, is considered. The associated system in involution is integrated in a parametric form. A…
The complete integrability of a generalized Riemann type hydrodynamic system is studied by means of symplectic and differential-algebraic tools. A compatible pair of polynomial Poissonian structures, Lax type representation and related…
We first reformulate para-statistics in terms of Lie-super triple systems. In this way, we reproduce various new kinds of para-statistics discovered recently by Palev in addition to the standard one. Also, bosonic and fermionic operators…
Liouville integrable systems, which have bi-Hamiltonian representation of the Gel'fand-Zakharevich type, are considered. Bi-presymplectic representation of one-Casimir bi-Hamiltonian chains and weakly bi-presymplectic representation of…
We obtain by dimensional reduction a $(1+1)$ supersymmetric system introduced in the description of ultracold quantum gases. The correct supercharges are identified and their algebra is constructed. Finally novel static self-dual solutions…
An integrable deformation of the well-known Neumann-Rosochatius system is studied by considering generalised bosonic spinning solutions on the eta-deformed AdS_5 x S^5 background. For this integrable model we construct a 4x4 Lax…
An application of approximate transformation groups to study dynamics of a system with distinct time scales is discussed. The utilization of the Krylov-Bogoliubov-Mitropolsky method of averaging to find solutions of the Lie equations is…
We present a first example of an integrable (3+1)-dimensional dispersionless system with nonisospectral Lax pair involving algebraic, rather than rational, dependence on the spectral parameter, thus showing that the class of integrable…
The matrix Sturm-Liouville equation on a finite interval with a Bessel-type singularity in the end of the interval is studied. Special fundamental systems of solutions for this equation are constructed: analytic Bessel-type solutions with…
The paper concerns the solvability by quadratures of linear differential systems, which is one of the questions of differential Galois theory. We consider systems with regular singular points as well as those with (non-resonant) irregular…
The Lie point symmetries and corresponding invariant solutions are obtained for a Gaussian, irrotational, compressible fluid flow. A supersymmetric extension of this model is then formulated through the use of a superspace and superfield…
We propose a highly efficient mixed quantum-classical molecular dynamics scheme based on a solution of the quantum-classical Liouville equation (QCLE). By casting the equations of motion for the quantum subsystem and classical bath degrees…