Related papers: A Spectral Analysis of the Nonlinear Schroedinger …
We consider the modulational instability of nonlinearly interacting two-dimensional waves in deep water, which are described by a pair of two-dimensional coupled nonlinear Schroedinger equations. We derive a nonlinear dispersion relation.…
We study the stability of an explicitly known, non-trivial self-similar blowup solution of the quadratic wave equation in the lowest energy supercritical dimension $d = 7$. This solution blows up at a single point and extends naturally away…
We study the existence and stability of localized states in the two-dimensional (2D) nonlinear Schrodinger (NLS)/Gross-Pitaevskii equation with a symmetric four-well potential. Using a fourmode approximation, we are able to trace the…
For the first time, the general nonlinear Schr\"odinger equation is investigated, in which the chromatic dispersion and potential are specified by two arbitrary functions. The equation in question is a natural generalization of a wide class…
We consider a non-relativistic quantum particle interacting with a singular potential supported by two parallel straight lines in the plane. We locate the essential spectrum under the hypothesis that the interaction asymptotically…
We study the asymptotic dynamics for solutions to a system of nonlinear Schr\"odinger equations with cubic interactions, arising in nonlinear optics. We provide sharp threshold criteria leading to global well-posedness and scattering of…
We investigate the nonisospectral effects of a semi-discrete nonlinear Schr\"{o}dinger equation, which is a direct integrable discretisation of its continuous counterpart. Bilinear form and double casoratian solution of the equation are…
We consider nonlinear Schr\"odinger equations in $\R^3$. Assume that the linear Hamiltonians have two bound states. For certain finite codimension subset in the space of initial data, we construct solutions converging to the excited states…
Using a Fourier spectral method, we provide a detailed numerically investigation of dispersive Schr\"odinger type equations involving a fractional Laplacian. By an appropriate choice of the dispersive exponent, both mass and energy sub- and…
We investigate the nonlinear Schr\"{o}dinger equation $iu_{t}+\Delta u+|u|^{p-1}u=0$ with $1+\frac{4}{N}<p<1+\frac{4}{N-2}$ (when $N=1, 2$, $1+\frac{4}{N}<p<\infty$) in energy space $H^1$ and study the divergent property of…
We report the first application of complex symmetric wavelets to the numerical simulation of a nonlinear signal propagation model. This model is the so-called nonlinear Schrodinger equation that describes, for instance, the evolution of the…
In this paper, we study a Schr\"odinger-type equation featuring a derivative in the nonlinear term and incorporating diffusion effects. This type of equation arises in various physical applications, such as modeling low-order magnetization…
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…
The propagation of an initially Gaussian wave packet of width $\Delta_0$ in a cubic non-linear Schrodinger equation with a negative coupling constant for the nonlinear term is considered . It is predicted analytically and verified…
In the present work we explore the potential of models of the discrete nonlinear Schr\"odinger (DNLS) type to support spatially localized and temporally quasiperiodic solutions on top of a finite background. Such solutions are rigorously…
It is proven that periodically varying and sign definite nonlinearity in a general case does not prevent collapse in two- and three-dimensional nonlinear Schrodinger equations: at any oscillation frequency of the nonlinearity blowing up…
We present what we believe to be the first known example of an exact quasiperiodic localized stable solution with spatially symmetric large-amplitude oscillations in a non-integrable Hamiltonian lattice model. The model is a one-dimensional…
We investigate the dynamical behavior of continuous and discrete Schrodinger systems exhibiting parity-time (PT) invariant nonlinearities. We show that such equations behave in a fundamentally different fashion than their nonlinear…
We consider the semiclassical (zero-dispersion) limit of the one-dimensional focusing Nonlinear Schroedinger equation (NLS) with decaying potentials. If a potential is a simple rapidly oscillating wave (the period has the order of the…
We show that the Schr\"{o}dinger-Newton equation, which describes the nonlinear time evolution of self-gravitating quantum matter, can be made compatible with the no-signaling requirement by elevating it to a stochastic differential…