Related papers: Time-relaxation structure-preserving explicit low-…
This paper is concerned with the numerical integration in time of nonlinear Schr\"odinger equations using different methods preserving the energy or a discrete analog of it. The Crank-Nicolson method is a well known method of order 2 but is…
In this paper, we develop an inverse scattering transform for the integrable focusing nonlinear Schr\"odinger (NLS) equation on the half-line subject to a class of boundary conditions. The method is based on the notions of integrable…
We consider the nonlinear Schr\"odinger equation with dispersion modulated by a (formal) derivative of a time-dependent function with fractional Sobolev regularity of class $W^{\alpha,2}$ for some $\alpha\in (0,1)$. Due to the loss of…
We extend to a specific class of systems of nonlinear Schr\"odinger equations (NLS) the theory of asymptotic stability of ground states already proved for the scalar NLS. Here the key point is the choice of an adequate system of modulation…
The nonlinear Schr{\"o}odinger (NLS) equation, which incorporates higher-order dispersive terms, is widely employed in the theoretical analysis of various physical phenomena. In this study, we explore the non-commutative extension of the…
A lattice version of quantum nonlinear Schrodinger (NLS) equation is considered, which has significantly simple form and fullfils most of the criteria desirable for such lattice variants of field models. Unlike most of the known lattice…
We study integrable boundary conditions associated with the whole hierarchy of nonlinear Schr\"{o}dinger (NLS) equations defined on the half-line. We find that the even order NLS equations and the odd order NLS equations admit rather…
In this paper, we study two kinds of structure-preserving splitting methods, including the Lie--Trotter type splitting method and the finite difference type method, for the stochasticlogarithmic Schr\"odinger equation (SlogS equation) via a…
The non-differentiability of the singular nonlinearity (such as $f=\ln|u|^2$) at $u=0$ presents significant challenges in devising accurate and efficient numerical schemes for the logarithmic Schr\"{o}dinger equation (LogSE). To address…
We study here the nonlinear Schrodinger Equation (NLS) as the first term in a sequence of approximations for an electromagnetic (EM) wave propagating according to the nonlinear Maxwell equations (NLM). The dielectric medium is assumed to be…
We study the modulational stability of the nonlinear Schr\"odinger equation (NLS) using a time-dependent variational approach. Within this framework, we derive ordinary differential equations (ODEs) for the time evolution of the amplitude…
Recently, an integrable system of coupled (2+1)-dimensional nonlinear Schrodinger (NLS) equations was introduced by Fokas (eq. (18) in Nonlinearity 29}, 319324 (2016)). Following this pattern, two integrable equations [eqs.2 and 3] with…
In this work, we investigate the existence and orbital (in)stability of several branches of standing--wave solutions for the cubic nonlinear Schr\"odinger equation (NLS) posed on a looping--edge graph $\mathcal{G}$, consisting of a circle…
In this paper, we generalize the exponential energy-preserving integrator proposed in the recent paper [SIAM J. Sci. Comput. 38(2016) A1876-A1895] for conservative systems, which now becomes linearly implicit by further utilizing the idea…
As a formal approximation, the nonlinear Schr\"{o}dinger (NLS) equation can be derived to describe the evolution of the envelopes of small oscillating wave packets-like solutions to the Euler-Poisson system. In this paper we rigorously…
We introduce a new class of integrators for stiff ODEs as well as SDEs. These integrators are (i) {\it Multiscale}: they are based on flow averaging and so do not fully resolve the fast variables and have a computational cost determined by…
In the present work, a nonlocal nonlinear Schr\"odinger (NLS) model is studied by means of a recent technique that identifies solutions of partial differential equations, by considering them as fixed points in {\it space-time}. This…
We discuss the stability of a class of normal forms of the completely resonant non--linear Schr\"odinger equation on a torus described in a previous paper. The discussion is essentially combinatorial and algebraic in nature. Thus this paper…
We consider a class of one dimensional Vector Nonlocal Non-linear Schr\"odinger Equation (VNNLSE) in an external complex potential with time-modulated Balanced Loss-Gain(BLG) and Linear Coupling(LC) among the components of Schr\"odinger…
A family of arbitrarily high-order fully discrete space-time finite element methods are proposed for the nonlinear Schr\"odinger equation based on the scalar auxiliary variable formulation, which consists of a Gauss collocation temporal…