Related papers: Variational approximations in discrete nonlinear S…
Using a variational approximation we study discrete solitons of a nonlinear Schroedinger lattice with a cubic-quintic nonlinearity. Using an ansatz with six parameters we are able to approximate bifurcations of asymmetric solutions…
We revisit the theme of non-nearest-neighbor interactions in nonlinear dynamical lattices, in the prototypical setting of the discrete nonlinear Schrodinger equation. Our approach offers a systematic way of analyzing the existence and…
From the mathematical side, nonlinear Schr\"odinger equations are usually investigated via variational methods, that cease to work in higher dimensions. This thesis tries to overcome this problem by focusing on spherically symmetric…
We analyse the structure of the exact, dark and bright soliton solutions of the driven non-linear Schr\"odinger equation. It is found that, a wide class of solutions of the higher order non-linear Schr\"odinger equation with a source can…
We examine a fractional version of the discrete Nonlinear Schr\"{o}dinger (dnls) equation, where the usual discrete laplacian is replaced by a fractional discrete laplacian. This leads to the replacement of the usual nearest-neighbor…
Travelling solitary waves in the one-dimensional discrete nonlinear Schr\"{o}dinger equation (DNLSE) with saturable onsite nonlinearity are studied. A variational approximation (VA) for the solitary waves is derived in an analytical form.…
We investigate bright solitons in the one-dimensional Schr\"odinger equation in the framework of an extended variational approach. We apply the latter to the stationary ground state of the system as well as to coherent collisions between…
A new integrable (2+1)-dimensional nonlocal nonlinear Schr\"odinger equation is proposed. The $N$-soliton solution is given by Gram type determinant. It is found that the localized N-soliton solution has interesting interaction behavior…
We consider the linear vector Schr\"odinger equation subjected to quadratic constraints. We demonstrate that the resulting nonlinear system is closely related to the Ablowitz-Ladik hierarchy and use this fact to derive the N-soliton…
We have applied a collocation approach to obtain the numerical solution to the stationary Schr\"odinger equation for systems of coupled oscillators. The dependence of the discretized Hamiltonian on scale and angle parameters is exploited to…
We discuss the behavior of solitary wave solutions of the nonlinear Schr{\"o}dinger equation (NLSE) as they interact with complex potentials, using a four parameter variational approximation based on a dissipation functional formulation of…
It is shown that the tight-binding approximation of the nonlinear Schr\"odinger equation with a periodic linear potential and periodic in space nonlinearity coefficient gives rise to a number of nonlinear lattices with complex, both linear…
We study four different approximations for finding the profile of discrete solitons in the one-dimensional Discrete Nonlinear Schr\"odinger (DNLS) Equation. Three of them are discrete approximations (namely, a variational approach, an…
Stationary and oscillatory bound states, or complexes, of the damped-driven solitons are numerically path-followed in the parameter space. We compile a chart of the two-soliton attractors, complementing the one-soliton attractor chart.
The novel inelastic collision properties of two-soliton interaction for an $n$-component coupled higher order nonlinear Schr\"odinger equation are studied. Some interesting features of three soliton interactions, related to the…
A mapping between stationary solutions of nonlinear Sch\"odinger equations with real and complex potentials is constructed and a set of exact solutions with real energies are obtained for a large class of complex potentials. As specific…
Exact analytical soliton solutions play an important role in soliton fields. Soliton solutions were obtained with some special constraints on the nonlinear parameters in nonlinear coupled systems, but they usually do not holds in real…
A variationally improved Sturmian approximation for solving time-independent Schr\"odinger equation is developed. This approximation is used to obtain the energy levels of a quartic anharmonic oscillator, a quartic potential, and a Gaussian…
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…
Integrable fractional equations such as the fractional Korteweg-deVries and nonlinear Schr\"odinger equations are key to the intersection of nonlinear dynamics and fractional calculus. In this manuscript, the first discrete/differential…