Related papers: On multichannel solutions of nonlinear Schr\"{o}di…
Based on our previous work for solving the nonlinear Schrodinger equation with multichannel dynamics that is given by a localized standing wave and radiation, in this work we deal with the multichannel solution which consists of a moving…
We apply the modulation theory to study the vortex and radiation solution in the two-dimensional nonlinear Schr\"{o}dinger equation. The full modulation equations which describe the dynamics of the vortex and radiation separately are…
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…
We consider a system of two discrete nonlinear Schr\"{o}dinger equations, coupled by nonlinear and linear terms. For various physically relevant cases, we derive a modulational instability criterion for plane-wave solutions. We also find…
Understanding, predicting, and controlling physical processes often relies on the analysis of the dynamics of partial differential equations (PDEs). In this context, the present study offers an in-depth investigation into the nonlinear…
In this paper, we consider a general form of nonlinear Schr\"{o}dinger equation with time-dependent nonlinearity. Based on the linear eigenvalue problem, the complete integrability of such nonlinear Schr\"{o}dinger equation is identified by…
In this work we apply point canonical transformations to solve some classes of nonautonomous nonlinear Schr\"{o}dinger equation namely, those which possess specific cubic and quintic - time and space dependent - nonlinearities. In this way…
In this paper, we report a more general class of nondegenerate soliton solutions, associated with two distinct wave numbers in different modes, for a certain class of physically important integrable two component nonlinear Schr\"{o}dinger…
We start a study of various nonlinear PDEs under the effect of a modulation in time of the dispersive term. In particular in this paper we consider the modulated non-linear Schr\"odinger equation (NLS) in dimension 1 and 2 and the…
We use the Riemann-Hilbert problem to study the interaction of the soliton with radiation in the parametrically driven, damped nonlinear Schr\"odinger equation. The analysis is reduced to the study of a finite-dimensional dynamical system…
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…
Based on recent ideas, stemming from the use of bubbles, we discuss an algorithm for the numerical simulation of the cubic nonlinear Schr{\"o}dinger equation with harmonic potential in any dimension, which could be easily extended to other…
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 investigate the multiplicity of nontrivial weak solutions for a class of complex equations. This class of problems are related with the existence of solitary waves for a nonlinear Sch\"{o}dinger equation. The main result is established…
The interaction between two co-propagating electrostatic wavepackets characterized by arbitrary carrier wavenumber is considered. A one-dimensional (1D) non-magnetized plasma model is adopted, consisting of a cold inertial ion fluid…
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…
Remarkable mathematical properties of the integrable nonlinear Schr\"odinger equation (NLSE) can offer advanced solutions for the mitigation of nonlinear signal distortions in optical fibre links. Fundamental optical soliton, continuous and…
We consider multiple solutions to the nonlinear Schr\"odinger equation (NLS) with a partial confinement, which is physically relevant to dynamics of the Bose-Einstein condensate. Our study not only verifies the existence of positive ground…
We study the presence of exact localized solutions in a quadratic-cubic nonlinear Schr\"odinger equation with inhomogeneous nonlinearities. Using a specific ansatz, we transform the nonautonomous nonlinear equation into an autonomous one,…
In this paper we develop a bilinearisation-reduction approach to derive solutions to the classical and nonlocal nonlinear Schr\"{o}dinger (NLS) equations with nonzero backgrounds. We start from the second order Ablowitz-Kaup-Newell-Segur…