Related papers: Generalization of the $\epsilon$-BBS and the Schen…
We develop a general classification of the infinite number of families of solitons and soliton complexes in the one-dimensional Gross-Pitaevskii/nonlinear Schrodinger equation with a nonlinear lattice pseudopotential, i.e., periodically…
In the first part of this paper, we express the generalized Bessel function associated with dihedral systems and a constant multiplicity function as a infinite series of confluent Horn functions. The key ingredient leading to this…
Using the point fusion procedure we obtain the new integrable systems from the Elliptic Schlesinger system (ESS). These new systems have the pole orders higher than one in the matrix of the Lax operator. Quadratic Poisson algebras on the…
We consider the full symmetric version of the Lax operator of the Toda lattice which is known as the full symmetric Toda lattice. The phase space of this system is the generic orbit of the coadjoint action of the Borel subgroup B^+(n) of…
It is well known that using the conventional non-Hermitian but ${\cal PT}-$symmetric Bose-Hubbard Hamiltonian with real spectrum one can realize the Bose-Einstein condensation (BEC) process in an exceptional-point limit of order $N$. Such…
We discuss an equivalence between the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formulation of the Einstein evolution equations, a subfamiliy of the Kidder--Scheel--Teukolsky formulation, and other strongly or symmetric hyperbolic first…
Applications of the theory and computations of boolean matrices are of fundamental importance to study a variety of discrete structural models. But the increasing ability of data collection systems to store huge volumes of multidimensional…
Patience Sorting is a combinatorial algorithm that can be viewed as an iterated, non-recursive form of the Schensted Insertion Algorithm. In recent work the authors have shown that Patience Sorting provides an algorithmic description for…
The main result of this paper is a generalization of the classical blossom algorithm for finding perfect matchings. Our algorithm can efficiently solve Boolean CSPs where each variable appears in exactly two constraints (we call it edge…
A Gaussian ansatz for the wave function of two-dimensional harmonically trapped anisotropic Bose-Einstein condensates is shown to lead, via a variational procedure, to a coupled system of two second-order, nonlinear ordinary differential…
A model for studying atomtronic devices and circuits based on finite temperature Bose-condensed gases is presented. The approach involves numerically solving equations of motion for atomic populations and coherences, derived using the…
Binary population synthesis (BPS) is an essential tool for extracting information about massive binary evolution from gravitational-wave (GW) detections of compact object mergers. It has been successfully used to constrain the most likely…
We introduce an exact classical algorithm for simulating Gaussian Boson Sampling (GBS). The complexity of the algorithm is exponential in the number of photons detected, which is itself a random variable. For a fixed number of modes, the…
The classical Toda flow is a well-known integrable Hamiltonian system that diagonalizes matrices. By keeping track of the distribution of entries and precise scattering asymptotics, one can exhibit matrix models for log-gases on the real…
The one-body reduced density matrix $\gamma$ plays a fundamental role in describing and predicting quantum features of bosonic systems, such as Bose-Einstein condensation. The recently proposed reduced density matrix functional theory for…
We consider a mixture of two distinct species of atoms of pseudospin-1/2 with both intraspecies and Interspecies spin-exchange interactions, and find all the ground stats in a general case of the parameters in the effective Hamiltonian. In…
The application of the conventional saddle-point approximation to condensed Bose gases is thwarted by the approach of the saddle-point to the ground-state singularity of the grand canonical partition function. We develop and test a variant…
New integrable lattice systems are introduced, their different integrable discretization are obtained. B\"acklund transformations between these new systems and the relativistic Toda lattice (in the both continuous and discrete time…
We consider a three spin component Bose Einstein Condensate as described by as many coupled nonlinear Schroedinger equations. For a very special ratio of the coupling constants, exact N soliton solutions to this set of equations are known.…
We consider abelian twisted loop Toda equations associated with the complex general linear groups. The Dodd--Bullough--Mikhailov equation is a simplest particular case of the equations under consideration. We construct new soliton solutions…