相关论文: Perturbative analysis of generally nonlocal spatia…
We construct deterministic particle solutions for linear and fast diffusion equations using a nonlocal approximation. We exploit the $2$-Wasserstein gradient flow structure of the equations in order to obtain the nonlocal approximating PDEs…
We study the interaction of (slowly modulated) high frequency waves for multi-dimensional nonlinear Schrodinger equations with gauge invariant power-law nonlinearities and non-local perturbations. The model includes the Davey--Stewartson…
We investigate the dynamics of travelling oscillating solitons of the cubic NLS equation under an external spatiotemporal forcing of the form $f(x,t) = a \exp[iK(t)x]$. For the case of time-independent forcing a stability criterion for…
We derive a class of discrete nonlinear Schr{\"o}dinger (DNLS) equations for general polynomial nonlinearity whose stationary solutions can be found from a reduced two-point algebraic problem. It is demonstrated that the derived class of…
Using similarity transformations we construct explicit nontrivial solutions of nonlinear Schr\"odinger equations with potentials and nonlinearities depending on time and on the spatial coordinates. We present the general theory and use it…
We address the interactions between optical solitons in the system with longitudinally varying nonlocality degree and nonlinearity strength. We consider a physical model describing light propagation in nematic liquid crystals featuring a…
We introduce a quasi-local integral functional and scalar quasi-local variables to examine a wide class of spherically symmetric inhomogeneous spacetimes that generalize the Lemaitre-Tolman-Bondi (LTB) dust solutions ("LTB" spacetimes). By…
The existence, stability and other dynamical properties of a new type of multi-dimensional (2D or 3D) solitons supported by a transverse low-dimensional (1D or 2D, respectively) periodic potential in the nonlinear Schr\"{o}dinger equation…
We consider the inviscid Leray-$\alpha$ equations - an inviscid nonlocal regularisation of the Euler equations. In the first part, we prove the convergence of strong solutions of the Leray-$\alpha$ equations to strong solutions of the Euler…
The dynamics of soliton pulses in the Nonlinear Schrodinger Equation (NLSE) driven by an external Traveling wave is studied analytically and numerically. The Hamiltonian structure of the system is used to show that, in the adiabatic…
We analyze the large-$n$ behavior of soliton solutions of the integrable focusing nonlinear Schr\"odinger equation with associated spectral data consisting of a single pair of conjugate poles of order $2n$. Starting from the zero…
We prove that the solutions to the discrete Nonlinear Schr\"odinger Equation (DNLSE) with non-local algebraically-decaying coupling converge strongly in $L^2(\mathbb{R}^2)$ to those of the continuum fractional Nonlinear Schr\"odinger…
Two-place nonlocal systems have attracted many scientists' attentions. In this paper, two-place non-localities are extended to multi-place non-localities. Especially, various two-place and four-place nonlocal nonlinear Schrodinger (NLS)…
We derive a closed expression for the spatial shift experienced by a black soliton colliding with a shallow dark soliton in the context of deformed non-linear Schr\"{o}dinger models. A perturbative scheme is developed based on the expansion…
We consider numerical instability that can be observed in simulations of localized solutions of the generalized nonlinear Schr\"odinger equation (NLS) by a split-step method where the linear part of the evolution is solved by a…
The time-dependent one-dimensional nonlinear Schr\"odinger equation (NLSE) is solved numerically by a hybrid pseudospectral-variational quantum algorithm that connects a pseudospectral step for the Hamiltonian term with a variational step…
We discuss differences between the variational approach to solitons and the accessible soliton approximaion in a highly nonlocal nonlinear medium. We compare results of both approximations by considering the same system of equations in the…
We study effects of nonlocality of the cubic self-focusing nonlinearity on the stability and symmetry-breaking bifurcation (SBB) of solitons in the model of a planar dual-core optical waveg- uide with nonlocal (thermal) nonlinearity. In…
We consider the nonlinear Schr{\"o}dinger equation (NLSE) in 1+1 dimension with scalar-scalar self interaction $\frac{g^2}{\kappa+1} (\psi^\star \psi)^{\kappa+1}$ in the presence of the external forcing terms of the form $r e^{-i(kx +…
We report results for solitons in models of waveguides with focusing or defocusing saturable nonlinearity and a parity-time(PT )-symmetric complex-valued external potential of the Scarf-II type. The model applies to the nonlinear wave…