相关论文: Existence of multi-solitons for the focusing Logar…
For both the cubic Nonlinear Schr\"odinger Equation (NLS) as well as the modified Korteweg-de Vries (mKdV) equation in one space dimension we consider the set ${\bf M}_N$ of pure $N$-soliton states, and their associated multisoliton…
We study the Derivative Nonlinear Schr\"odinger equation for generic initial data in a weighted Sobolev space that can support bright solitons (but exclude spectral singularities). Drawing on previous well-posedness results, we give a full…
In this article we consider the Cauchy problem for the cubic focusing nonlinear Schr\"o\-dinger (NLS) equation on the line with initial datum close to a particular $N$-soliton. Using inverse scattering and the $\bar{\partial}$ method we…
Multi-soliton solutions, i.e. solutions behaving as the sum of N given solitons as $t\to +\infty$, were constructed in previous works for the L2 critical and subcritical (NLS) and (gKdV) equations. In this paper, we extend the construction…
We prove the existence of multi-soliton solutions for the nonlinear Schr\"{o}dinger equation with repulsive Dirac delta potential and $L^2$-supercritical focusing nonlinear term. Our main contribution is to treat the unmoving part of the…
By introducing and solving two correlative constrained variational problems as well as spectrum analysis, an approach to fix soliton frequency from the prescribed mass for nonlinear Schr\"odinger equations is found, and an open problem in…
The soliton resolution conjecture for the focusing nonlinear Schrodinger equation (NLS) is the vaguely worded claim that a global solution of the NLS, for generic initial data, will eventually resolve into a radiation component that…
In this paper, we establish the orbital stability of the 1-soliton solution for the derivative nonlinear Schr\"odinger equation under perturbations in $L^2(\mathbb{R})$. We demonstrate this stability by utilizing the B\"acklund…
We study soliton solutions of a modified non-linear Schroedinger (MNLS) equation. Using an Ansatz for the time and azimuthal angle dependence previously considered in the studies of the spinning Q-balls, we construct multi-node solutions of…
We consider the nonlinear Schr\"odinger equation with a focusing cubic term and a defocusing quintic nonlinearity in dimensions two and three. The core of this article is the notion of stability of solitary waves. We recall the two standard…
In this paper, we introduce the reverse-space and reverse-space-time nonlocal discrete derivative nonlinear Schr\"odinger (DNLS) equations through the nonlocal symmetry reductions of the semi-discrete Gerdjikov-Ivanov equation. The…
We consider a coupled system of nonlinear Lowest Landau Level equations. We first show the existence of multi-solitons with an exponentially localised error term in space, and then we prove a uniqueness result. We also show a long time…
We study the Cauchy problem for the focusing nonlinear Schrodinger (NLS) equation. Using the DBAR generalization of the nonlinear steepest descent method we compute the long time asymptotic expansion of the solution in any fixed space-time…
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 present the results of a numerical experiment inspired by the semiclassical (zero-dispersion) limit of the focusing nonlinear Schroedinger (NLS) equation. In particular, we focus on the Gaussian semiclassical soliton ensemble, a family…
We consider a system of coupled cubic Schr\"odinger equations in one space dimension \begin{equation*} \begin{cases} i \partial_t u + \partial_x^2 u +(|u|^2 + \omega |v|^2) u =0\\ i \partial_t v + \partial_x^2 v+ (|v|^2 + \omega |u|^2) v=0…
We found a new kind of soliton solutions for the 5-parameter family of the potential-free Stenflo-Sabatier-Doebner-Goldin nonlinear modifications of the Schr\"odinger equation. In contradistinction to the "usual'' solitons like…
We review some recent results concerning Gibbs measures for nonlinear Schroedinger equations (NLS), with implications for the theory of the NLS, including stability and typicality of solitary wave structures. In particular, we discuss the…
A generalized inhomogeneous higher-order nonlinear Schrodinger (GIHNLS) equation for the Heisenberg ferromagnetic spin chain system in (1+1)-dimensions under zero boundary condition at infinity is taken into account. The spectral analysis…
We consider the nonlinear Schrodinger equation with a logarithmic nonlinearity in a dispersive regime. We show that the presence of the nonlinearity affects the large time behavior of the solution: the dispersion is faster than usual by a…