Related papers: Application of the quadratures method to the NLS w…
By using AKNS scheme and soliton connection taking values in N=1 superconformal algebra we obtain new coupled super Nonlinear Schrodinger equations.
Using similarity transformations we construct explicit solutions of the nonlinear Schrodinger equation with linear and nonlinear periodic potentials. We present explicit forms of spatially localized and periodic solutions, and study their…
In this paper, we study a couple of NLS equations characterized by mixed cubic and superlinear power laws. Classification of the solutions as well as existence and uniqueness of the steady state solutions have been investigated.
A novel kind of shape changing (intensity redistribution) collision with potential application to signal amplification is identified in the integrable $N$-coupled nonlinear Schr{\"o}dinger (CNLS) equations with mixed signs of focusing and…
We study systematically the scattering of solitons on localized impurities in the discrete nonlinear Schr\"odinger (DNLS) equation with a saturable nonlinearity. We show that, apart from the generic scenario of the outcome of the scattering…
A method to find exact solutions to nonlinear Schr\"odinger equation, defined on a line and on a plane, is found by connecting it with second order linear ordinary differential equation. The connection is essentially made using Riccati…
The effective long-time dynamics of solitary wave solutions of the nonlinear Schr\"odinger equation in the presence of rough nonlinear perturbations is rigorously studied. It is shown that, if the initial state is close to a slowly…
The Darboux transformation (DT) formulae for the derivative nonlinear Schr\"{o}dinger (DNLS) equation are expressed in concise forms, from which the multi-solitons, n-periodic solutions, higher-order hybrid-pattern solitons and some mixed…
We obtain new coupled super Nonlinear Schrodinger equations by using AKNS scheme and soliton connection taking values in N=2 superconformal algebra.
In a previous paper (Matsuno 2011 {\it J. Phys. A: Math. Theore.} {\bf 44} 495202), we have presented a determinantal expression of the bright $N$-soliton solution for a multi-component modified nonlinear Schr\"odinger (NLS) system with…
We derive an exact solution to the local nonlinear Schr\"odinger equation (NLSE) using the Darboux transformation method. The new solution describes the profile and dynamics of a two-soliton molecule. Using an algebraically-decaying seed…
We consider equations of nonlinear Schrodinger type augmented by nonlinear damping terms. We show that nonlinear damping prevents finite time blow-up in several situations, which we describe. We also prove that the presence of a quadratic…
In this result, we develop the techniques of \cite{KS1} and \cite{BW} in order to determine a class of stable perturbations for a minimal mass soliton solution of a saturated, focusing nonlinear Schr\"odinger equation {c} i u_t + \Delta u +…
Solitons are ubiquitous in nature and play a pivotal role in the structure and dynamics of solutions of nonlinear propagation equations. In many instances where solitons exist, analytical expressions of these special objects are not…
In this paper we study dynamics of solitons in the generalized nonlinear Schr\"odinger equation (NLS) with an external potential in all dimensions except for 2. For a certain class of nonlinearities such an equation has solutions which are…
We study the non-linear Schroedinger equation in (1+1) dimensions in which the nonlinear term is taken in the form of a nonlocal interaction of the Coulomb or Yukawa-type. We solve the equation numerically and find that, for all values of…
We prove the uniqueness and non-degeneracy of positive solutions to a cubic nonlinear Schr\"odinger (NLS) type equation that describes nucleons. The main difficulty stems from the fact that the mass depends on the solution itself. As an…
We further develop the method of dressing the boundary for the focusing nonlinear Schr\"odinger equation (NLS) on the half-line to include the new boundary condition presented by Zambon. Additionally, the foundation to compare the solutions…
In this paper we show a systematical method to obtain exact solutions of the nonautonomous nonlinear Schr\"odinger (NLS) equation. An integrable condition is first obtained by the Painlev\`e analysis, which is shown to be consistent with…
We demonstrate the systematic derivation of a class of discretizations of nonlinear Schr{\"o}dinger (NLS) equations for general polynomial nonlinearity whose stationary solutions can be found from a reduced two-point algebraic condition. We…