相关论文: Near soliton dynamics and singularity formation fo…
In this article we study some aspects of dispersive and concentration phenomena for the Schr\"odinger equation posed on hyperbolic space $\mathbb{H}^n$, in order to see if the negative curvature of the manifold gets the dynamics more stable…
We study the focusing $L^2$-critical and supercritical stochastic nonlinear Schr\"odinger equation subject to additive or multiplicative noise. We investigate global or long time behavior of solutions in $H^1$, which would correspond to…
We consider the focusing nonlinear Schr\"odinger equations $i\partial_t u+\Delta u +u|u|^{p-1}=0$ in dimension $1\leq N\leq 5$ and for slightly $L^2$ supercritical nonlinearities $p_c<p<(1+\e)p_c$ with $p_c=1+\frac{4}{N}$ and $0<\e\ll 1$.…
We consider the problem of the soliton propagation, in a slowly varying medium, for a generalized, variable-coefficients nonlinear Schr\"odinger equation. We prove existence and uniqueness of new soliton-like solutions for a large class of…
We consider a class of Fokker--Planck equations with linear diffusion and superlinear drift enjoying a formal Wasserstein-like gradient flow structure with convex mobility function. In the drift-dominant regime, the equations have a finite…
The term "direct scattering study" refers to the calculation and analysis of the discrete eigenvalues of the associated Zakharov-Shabat (ZS) eigenvalue problem. The direct scattering study was applied to time-dependent oscillating solitons…
We consider the Cauchy problem for the $L^2$-critical nonlinear Schr\"odinger equation with a fractional dissipation. According to the order of the fractional dissipation, we prove the global existence or the existence of finite time blowup…
The question of collapse (blow-up) in finite time is investigated for the two-dimensional (non-integrable) space-time nonlocal nonlinear Schrodinger equations. Starting from the two-dimensional extension of the well known AKNS q,r system,…
For nonlinear dispersive systems, the nonlinear Schr\"odinger (NLS) equation can usually be derived as a formal approximation equation describing slow spatial and temporal modulations of the envelope of a spatially and temporally…
In this paper we study the long time behavior of a discrete approximation in time and space of the cubic nonlinear Schr\"odinger equation on the real line. More precisely, we consider a symplectic time splitting integrator applied to a…
We consider KdV-type equations with $C^1$ nonhomogeneous nonlinearities and small dispersion $\varepsilon$. The first result consists in the conclusion that, in the leading term with respect to $\varepsilon$, the solitary waves in this…
I analyze the one-dimensional, cubic Schr\"odinger equation, with nonlinearity constructed from the current density, rather than, as is usual, from the charge density. A soliton solution is found, where the soliton moves only in one…
Static soliton bound states in nonlinear systems are investigated analytically and numerically in the framework of the parametrically driven, damped nonlinear Schr\"odinger equation. We find that the ordinary differential equations, which…
We consider the generalized Korteweg-de Vries equation in the supercritical case, and we are interested in solutions which converge to a soliton in large time in H^1. In the subcritical case, such solutions are forced to be exactly solitons…
We consider the mass-subcritical nonlinear Schr\"odinger equation in all space dimensions with focusing or defocusing nonlinearity. For such equations with critical regularity $s_c\in(\max\{-1,-\frac{d}{2}\},0)$, we prove that any solution…
We present a collective coordinate approximation to model the dynamics of two interacting nonlinear Schr\"odinger (NLS) solitons. We discuss the accuracy of this approximation by comparing our results to those of the full numerical…
In this article, we establish in the radial framework the $H^1$-scattering for the critical 2-D nonlinear Schr\"odinger equation with exponential growth. Our strategy relies on both the a priori estimate derived in \cite{CGT, PV} and the…
Assuming that the nucleus can be treated as a perfect fluid we study the conditions for the formation and propagation of Korteweg-de Vries (KdV) solitons in nuclear matter. The KdV equation is obtained from the Euler and continuity…
We establish the classification of minimal mass blow-up solutions of the $L^2$ critical inhomogeneous nonlinear Schr\"odinger equation \[ i\partial_t u + \Delta u + |x|^{-b}|u|^{\frac{4-2b}{N}}u = 0, \] thereby extending the celebrated…
We investigate the validity of a soliton dynamics behavior in the semi-relativistic limit for the nonlinear Schr\"odinger equation in $\R^{N}, N\ge 3$, in presence of a singular external potential.