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In this paper we propose a method which provides a full description of solitary wave solutions of the Schroedinger equation with periodically varying dispersion. This method is based on analysis and polynomial deformation of the spectrum of…
Bilinear systems of equations are defined, motivated and analyzed for solvability. Elementary structure is mentioned and it is shown that all solutions may be obtained as rank one completions of a linear matrix polynomial derived from…
A dispersion-managed optical system with step-wise periodical variation of dispersion is studied in a strong dispersion map limit in the framework of path-averaged Gabitov-Turitsyn equation. The soliton solution is obtained by iterating the…
The dispersion-managed (DM) optical system with step-wise periodical variation of dispersion is studied in the framework of path-averaged Gabitov-Turitsyn equation. The soliton solution is obtained by iterating the path-averaged equation.…
The $N$-soliton solution is presented for a two-component modified nonlinear Schr\"odinger equation which describes the propagation of short pulses in birefringent optical fibers. The solution is found to be expressed in terms of…
In this paper, we propose two iterative methods for finding a common solution of a finite family of equilibrium problems for pseudomonotone bifunctions. The first is a parallel hybrid extragradient-cutting algorithm which is extended from…
We analyze the BPS solutions of minimal supergravity coupled to an anti-self-dual tensor multiplet in six dimensions and find solutions that fluctuate non-trivially as a function of two variables. We consider families of solutions coming…
Bimonotone subdivisions in two dimensions are subdivisions all of whose sides are either vertical or have nonnegative slope. They correspond to statistical estimates of probability distributions of strongly positively dependent random…
Reciprocal space methods for solving Poisson's equation for finite charge distributions are investigated. Improvements to previous proposals are presented, and their performance is compared in the context of a real-space density functional…
In this paper we develop a very general class of bivariate discrete distributions. The basic idea is very simple. The marginals are obtained by taking the random geometric sum of a baseline distribution function. The proposed class of…
Recently in [Phys. Rev. B 99, 241301(R) (2019)] tensor networks build upon logical circuits were briefly introduced to retrieve exciton and biexciton states. Compared to a conventional approach the tensor network methods scales logarithmic…
We study by first principle computer simulations the low temperature phase diagram of bosonic dipolar gases in a bilayer geometry, as a function of the two control parameters, i.e., the in-plane density and the interlayer distance. We…
Summary: A system of autonomous ordinary differential equations depending on a small parameter is considered such that the unperturbed system has an invariant manifold of periodic solutions that is not normally hyperbolic but is normally…
Families of solutions to the field equations of the covariant BRST invariant effective action of the membrane theory are constructed. The equations are discussed in a double dimensional reduction, they lead to a nonlinear equation for a one…
We use the circle method to count the number of integer solutions to systems of bihomogeneous equations of bidegree $(1,1)$ and $(2,1)$ of bounded height in lopsided boxes. Previously, adjusting Birch's techniques to the bihomogeneous…
Tensor B-spline methods are a high-performance alternative to solve partial differential equations (PDEs). This paper gives an overview on the principles of Tensor B-spline methodology, shows their use and analyzes their performance in…
The algebraic characterization of dual univariate interpolating subdivision schemes is investigated. Specifically, we provide a constructive approach for finding dual univariate interpolating subdivision schemes based on the solutions of…
Two integrable differential-difference equations are derived from a (2+1)-dimensional modified Heisenberg ferromagnetic equation and a resonant nonlinear Schr\"oinger equation respectively. Multi-soliton solutions of the resulted…
We propose that stable boson stars generically fall within an infinite-parameter family of solutions that oscillate on any number of non-commensurate frequencies. We numerically construct two-frequency solutions and explore their parameter…
In this paper we detail the mechanisms that drive substitutional binary diffusion and derive appropriate governing equations. We focus on the one-dimensional case with insulated boundary conditions. Asymptotic expansions are used in order…