Related papers: Small-amplitude excitations in a deformable discre…
We found a new kind of soliton solutions for the 5-parameter family of the potential-free Stenflo-Sabatier-Doebner-Goldin nonlinear modifications of the Schr\"odinger equation. In contradistinction to the "usual'' solitons like…
We study the stability, form and interaction of single and multiple dark solitons in quasi-one-dimensional dipolar Bose-Einstein condensates. The solitons are found numerically as stationary solutions in the moving frame of a non-local…
In this paper, we are concerned with a a semi-discrete complex short pulse (CSP) equation of both focusing and defocusing types, which can be viewed as an analogue to the Ablowitz-Ladik (AL) lattice in the ultra-short pulse regime. By using…
We study the cubic- (focusing-)quintic (defocusing) nonlinear Schr\"odinger equation in two transverse dimensions. We discuss a family of stationary traveling waves, including rarefaction pulses and vortexantivortex pairs, in a background…
The asymptotic of the solution of the discrete Wheeler-DeWitt equation is found in the vicinity of small scale factors. It is shown that this problem is equivalent to the solution of the stationary Schr\"{o}dinger equation in the (super)…
We consider the defocusing nonlinear Schr{\"o}dinger equation in several space dimensions, in the presence of an external potential depending on only one space vari-able. This potential is bounded from below, and may grow arbitrarily fast…
The stability and collapse of fundamental unstaggered bright solitons in the discrete Schrodinger equation with the nonpolynomial on-site nonlinearity, which models a nearly one-dimensional Bose-Einstein condensate trapped in a deep optical…
In this paper we study microlocal singularities of solutions to Schrodinger equations on scattering manifolds, i.e., noncompact Riemannian manifolds with asymptotically conic ends. We characterize the wave front set of the solutions in…
Families of soliton pairs, namely vector solitons, are found within the context of a coupled nonlocal nonlinear Schrodinger system of equations, as appropriate for modeling beam propagation in nematic liquid crystals. In the focusing case,…
An application of the Darboux transformation on a cnoidal wave background in the coupled nonlinear Schr\"{o}dinger equation gives a new solution which describes a soliton moving on a cnoidal wave. This is a generalized version of the…
We study the stochastic nonlinear Schroedinger equations with linear multiplicative noise, particularly in the defocusing mass-critical and energy-critical cases. For general initial data, we prove the global existence and uniqueness of…
We consider a parametrically driven Klein--Gordon system describing micro- and nano-devices, with integrated electrical and mechanical functionality. Using a multiscale expansion method we reduce the system to a discrete nonlinear…
In the present work, we examine "binary" waveguide arrays, where the coupling between adjacent sites alternates between two distinct values $C_1$ and $C_2$ and a saturable nonlinearity is present on each site. Motivated by experimental…
We consider a system of generalized coupled Discrete Nonlinear Schr\"{o}dinger (DNLS) equations, derived as a tight-binding model from the Gross-Pitaevskii-type equations describing a zigzag chain of weakly coupled condensates of…
Group velocity and group velocity dispersion for a wave packet in vectorial discrete Klein-Gordon models are obtained by an expansion, based on perturbation theory, of the linear system giving the dispersion relation and the normal modes.…
An analysis of discrete systems is important for understanding of various physical processes, such as excitations in crystal lattices and molecular chains, the light propagation in waveguide arrays, and the dynamics of Bose-condensate…
The method of multiscale analysis is constructed for dicrete systems of evolution equations for which the problem is that of the far behavior of an input boundary datum. Discrete slow space variables are introduced in a general setting and…
We study the connection problem for a class of linear differential equations of order $N$ closely related to the Baxter equation of the quantum Toda chain. The space of solutions is $N$-dimensional and several linearly independent solutions…
Under certain mode-matching conditions, small-amplitude waves can be trapped by coupling to solitons of nonlinear fields. We present a model for this phenomenon, consisting of a linear equation coupled to the Korteweg-de Vries equation. The…
For the first time, the general nonlinear Schr\"odinger equation is investigated, in which the chromatic dispersion and potential are specified by two arbitrary functions. The equation in question is a natural generalization of a wide class…