Related papers: Symmetries for exact solutions to the nonlinear Sc…
Invariants of nonlinear gauge transformations of a family of nonlinear Schr\"odinger equations proposed by Doebner and Goldin are used to characterize the behaviour of exact solutions of these equations.
The nonlinear Schr\"{o}dinger-Newton system \begin{equation*} \begin{cases} \Delta u- V(|x|)u + \Psi u=0, &~x\in\mathbb{R}^3,\\ \Delta \Psi+\frac12 u^2=0, &~x\in\mathbb{R}^3, \end{cases} \end{equation*} is a nonlinear system obtained by…
The numerical approximation of low-regularity solutions to the nonlinear Schr\"odinger equation is notoriously difficult and even more so if structure-preserving schemes are sought. Recent works have been successful in establishing…
In this paper, we investigate the space-time shifted nonlocal derivative nonlinear Schr\"{o}dinger (DNLS) equation under nonzero boundary conditions using the Riemann--Hilbert (RH) approach for the first time. To begin with, in the direct…
We consider the Cauchy problem for the nonlinear Schroedinger eqiation with initial data close to a sum of N decoupled solitons. Under some suitable assumptions on the spectral structure of the one soliton linearizations we prove that for…
We carry out a group-theoretical study of the pair of nonlinear Schr\"{o}dinger equations describing the propagation of waves in nonlinear birefringent optical fibers. We exploit the symmetry algebra associated with these equations to…
In this paper we announce the result of asymptotic dynamics of solitons of nonlinear Schrodinger equations with external potentials. To each local minima of the potential there is a soliton centered around it. Under some conditions on the…
We study the initial-value problem for the nonlinear Schr\"odinger equation. Application of the inverse scattering transform method involves solving direct and inverse scattering problems for the Zakharov-Shabat system with complex…
We construct one soliton solutions for the nonlinear Schroedinger equation with variable quadratic Hamiltonians in a unified form by taking advantage of a complete (super) integrability of generalized harmonic oscillators. The soliton wave…
In this paper the long-time dynamics of the massive Thirring model is investigated. Firstly the nonlinear steepest descent method for Riemann-Hilbert problem is explored to obtain the soliton resolution of the solutions to the massive…
Dynamics of solitons is considered in an extended nonlinear Schr\"odinger equation, including a pseudo-stimulated-Raman-scattering (pseudo-SRS) term (scattering on damping low-frequency waves, third-order dispersion (TOD) and inhomogeneity…
Existence of a positive solution for a class of nonlinear Schr\"odinger equations with potentials which decay to zero at infinity, with an appropriate rate, approaching zero mass type limit scalar field equations, is established via a new…
In this paper, the inverse scattering transform for the integrable discrete nonlocal PT symmetric nonlinear Schr\"odinger equation with nonzero boundary conditions is presented. According to the two different signs of symmetry reduction and…
A generalized nonlinear Schr\"odinger equation admits WTC formal solutions as was shown by Clarkson. We show that they are convergent and determine real-analytic solutions near a noncharacteristic, movable singularity manifold.
In this paper, by means of similarity transformations we study exact analytical solutions for a generalized nonlinear Schr$\ddot{\mbox{o}}$dinger equation with variable coefficients. This equation appears in literature describing the…
We perform the analysis of the focusing nonlinear Schr\"odinger equation on the half-line with time-dependent boundary conditions along the lines of the nonlinear method of images with the help of B\"acklund transformations. The difficulty…
The authors give a detailed information about symmetry (Lie, non-Lie, conditional) of nonlinear PDEs for spinor, vector and scalar fields; using advanced methods of group-theoretical, symmetry analysis construct wide families of classical…
In this paper a nonlinear coupled Schrodinger system in the presence of mixed cubic and superlinear power laws is considered. Focus are made on the steady state solutions of the continuous system for existence and uniqueness by minimizing…
We prove the existence of non-trivial solutions to a system of coupled, nonlinear, Schroedinger equations with general nonlinearity.
The integrable vector nonlinear Schrodinger (vector NLS) equation is investigated by using Zakharov-Shabat (ZS) scheme. We get a Lax pair formulation of the vector NLS model. Multi-soliton solution of the equation is also derived by using…