Related papers: Beyond Nonlinear Schr\"odinger Equation Approximat…
Quasi-periodic solutions with Liouvillean frequency of forced nonlinear Schr\"odinger equation are constructed. This is based on an infinite dimensional KAM theory for Liouvillean frequency.
Assessment of the degree of boundedness/stability of multidimensional nonlinear systems with time-dependent and nonperiodic coefficients is an important problem in various applied areas which has no adequate resolution yet. Most of the…
The electromagnetic nonlinear Schr\"odinger (emNLS) equation is a variant of the well-studied nonlinear Schr\"odinger equation. In this article, we consider questions of global existence or blow-up for emNLS in dimensions 3 and higher.
The acoustic wave-propagation without mean flow and heat flux can be described in terms of velocity and pressure by the compressible nonlinear Navier-Stokes equations, where boundary layers appear at walls due to the viscosity and a…
We consider an integrable generalization of the nonlinear Schr\"odinger (NLS) equation that was recently derived by one of the authors using bi-Hamiltonian methods. This equation is related to the NLS equation in the same way that the…
We consider {\it small solutions} of a vibrating system with smooth non-linearities for which we provide an approximate solution by using a double scale analysis; a rigorous proof of convergence of a double scale expansion is included; for…
Fractional nonlinear differential equations present an interplay between two common and important effective descriptions used to simplify high dimensional or more complicated theories: nonlinearity and fractional derivatives. These…
We introduce and analyze a symmetric low-regularity scheme for the nonlinear Schr\"odinger (NLS) equation beyond classical Fourier-based techniques. We show fractional convergence of the scheme in $L^2$-norm, from first up to second order,…
We show that the complex modified KdV (cmKdV) equation and generalized nonlinear Schr\"odinger (GNLS) equation belong to the Ablowitz, Kaup, Newell and Segur or so-called AKNS hierarchy. Both equations do not follow from the action…
On a smooth, closed Riemannian manifold, we study the question of proportionality of components, also called synchronization, of vector-valued solutions to nonlinear elliptic Schr\"odinger systems with constant coefficients. In particular,…
The dynamics of models described by a one-dimensional discrete nonlinear Schr\"odinger equation is studied. The nonlinearity in these models appears due to the coupling of the electronic motion to optical oscillators which are treated in…
We consider the focusing inhomogeneous nonlinear Schr\"odinger equation in $H^1(\mathbb{R}^3)$, \begin{equation} i\partial_t u + \Delta u + |x|^{-b}|u|^{2}u=0,{equation} where $0 < b <\tfrac{1}{2}$. Previous works have established a…
In this paper, we investigate a general integrable nonlocal coupled nonlinear schr\"odinger (NLS) system with the the parity-time (PT) symmetry, which contains not only the nonlocal self-phase modulation and the nonlocal cross-phase…
The nonlinear Schroedinger model is a prototypical dispersive wave equation that features finite time blowup, either for supercritical exponents (for fixed dimension) or for supercritical dimensions (for fixed nonlinearity exponent). Upon…
In this paper, an extended nonlinear Schrodinger equation with higher-order that includes fifth-order dispersion with matching higher-order nonlinear terms is investigated under zero boundary condition at infinity. Carrying out the spectral…
In the present work we provide a characterization of the ground states of a higher-dimensional quadratic-quartic model of the nonlinear Schr{\"o}dinger class with a combination of a focusing biharmonic operator with either an isotropic or…
By using AKNS scheme and soliton connection taking values in N=1 superconformal algebra we obtain new coupled super Nonlinear Schrodinger equations.
In this article, we study the Anderson Hamiltonian in the full space and prove wellposedness of nonlinear stochastic wave equation and NLS with polynomial nonlinearities.
This article is devoted to the construction of new numerical methods for the semiclassical Schr\"odinger equation. A phase-amplitude reformulation of the equation is described where the Planck constant epsilon is not a singular parameter.…
The nonlinear Schr\"odinger equation (NLSE) is a rich and versatile model, which in one spatial dimension has stationary solutions similar to those of the linear Schr\"odinger equation as well as more exotic solutions such as solitary waves…