It is shown that the collective nonlinear interactions between intense neutrino or anti-neutrino fluxes and a dense neutrino plasma are governed by a multidimensional coupled cubic Schrödinger equation in which the interaction potential is positive or negative depending on the neutrino type. The cubic Schrödinger equation describes the splitting and focusing of intense neutrino beams due to the...

This paper presents a simple and fast recurrence equation-based method for solving the cubic spline interpolation problem. The computational complexity of the method is O(n), where n is the number of measurements. The recurrence equation-based method is illustrated by an example that estimates the movement of a moving object. The paper also describes a MATLAB implementation of the new method an...

We study the stability of traveling waves of nonlinear Schrödinger equation with nonzero condition at infinity obtained via a constrained variational approach. Two important physical models are Gross-Pitaevskii (GP) equation and cubic-quintic equation. First, under a non-degeneracy condition we prove a sharp instability criterion for 3D traveling waves of (GP), which had been conjectured in the...

In this paper we unify the two subjects of implicitization and parametrization of nonsingular cubic surfaces. Beginning with a cubic parametrization with six basepoints, we first form a three by four Hilbert–Burch matrix, and then a three by three matrix of linear forms whose determinant is the implicit equation. Beginning with an implicit equation, we show how to construct a three by three mat...

time-dependent schrödinger equation for a 1-d model of hydrogen molecular ion h2+ in intenselaser field linearly polarized along the molecular axis is solved. ionization rates are calculated for differentinitial states. the evolution of electronic wavefunction at fixed inter-nuclear separations are simulated andanalyzed. the results obtained for the ground state of this 1-d model of h2+ show ap...

We study controllability of 2D defocusing cubic Schroedinger equation under periodic boundary conditions and control applied via source term (additively). The source term is a linear combination of few complex exponentials (modes) with time-variant coefficients controls. We manage to prove that controlling just 4 modes one can achieve controllability of this equation in any finite-dimensional p...

For the semi-classical limit of the cubic, defocusing nonlinear Schrödinger equation with an external potential, we explain the notion of criticality before a caustic is formed. In the sub-critical and critical cases, we justify the WKB approximation. In the super-critical case, the WKB analysis provides a new phenomenon for the (classical) cubic, defocusing nonlinear Schrödinger equation, whic...

We consider in this work the initial value problem for the one dimensional cubic nonlinear Schrödinger equation. In order to integrate it numerically, one option frequently used, is to impose local absorbing boundary conditions. A finite element discretization in space of the cubic nonlinear Schrödinger equation is considered along with the absorbing boundary conditions obtained for an analogou...

We discuss, with illustrations, some physical significances of fifth-order nonlinear susceptibility for pulse dynamics in monomode optical fibres. The amplitude dynamic governing equation is the cubic-quintic nonlinear Schrödinger equation, (CQNLSE), which has soliton properties similar to the cubic nonlinear Schrödinger equation, (CNLSE), based on solutions by a variational method. Some differ...

In this piece of work, using three spatial grid points, we discuss a new two-level implicit cubic spline method of O(k + kh + h) for the solution of quasi-linear parabolic equation   , , , , xx x t u f x t u u u  , 0< x <1, t > 0 subject to appropriate initial and Dirichlet boundary conditions, where h > 0, k > 0 are grid sizes in space and time-directions, respectively. The cubic spline app...