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...

Let k be a field of characteristic 6= 2. We survey a general method of the field intersection problem of generic polynomials via formal Tschirnhausen transformation. We announce some of our recent results of cubic, quartic and quintic cases the details of which are to appear elsewhere. In this note, we give an explicit answer to the problem in the cases of cubic and dihedral quintic by using mu...

Abstract Spiral segments are useful in the design of fair curves. They are important in CAD/CAM applications, the design of highway and railway routes, trajectories of mobile robots and other similar applications. The quintic Pythagorean hodograph (PH) curve discussed in this technical report is polynomial; it has the attractive properties that its arc-length is a polynomial of its parameter, a...

We study degenerations of Kummer surfaces associated to certain divisors in Nieto’s quintic threefold and show how they arise from boundary components of a suitable toroidal compactification of the corresponding Siegel modular threefold. The aim of this paper is to study the degenerations of an interesting class of Kummer surfaces in P in terms of degenerations of the corresponding abelian surf...

Abstract In this study, the time-dependent potential coefficient in a higher-order PDE with initial and boundary conditions is numerically constructed for first time from nonlocal integral condition. Even though inverse identification problem investigated study ill-posed, it has unique solution. For discretizing direct finding stable accurate solutions, we employ Quintic B-spline (QBS) collocat...

A new approach for the geometrical optimization of five-axis-movement is presented in this paper. Regarding a fiveaxis-movement with large tolerances for lead and tilt-angle for example in the case of laser-cutting there are endless ways of generating motions without violating the orientation-tolerances. By regarding the movement of the involved axes it is shown that for a given 5-axis trajecto...

We introduce a one-dimensional phenomenological model of a nonlocal medium featuring focusing cubic and defocusing quintic nonlocal optical nonlinearities. By means of numerical methods, we find families of solitons of two types, even-parity (fundamental) and dipole-mode (odd-parity) ones. Stability of the solitons is explored by means of computation of eigenvalues associated with modes of smal...

This paper introduces an extension of the time-splitting sine-spectral (TSSP) method for solving damped focusing nonlinear Schrödinger equations (NLSs). The method is explicit, unconditionally stable, and time transversal invariant. Moreover, it preserves the exact decay rate for the normalization of the wave function if linear damping terms are added to the NLS. Extensive numerical tests are p...

In [4] the first named author discussed the explicit solutions of the cubic spline interpolation problems. We are now concerned with quintic spline functions. Let 5B[0, n] denote the class of quintic spline functions S(x) defined in the interval [0, n] and having the points 0, 1, • • • , n — 1 as knots. This means that the restriction of S(x) to the interval (*>, J > + 1 ) (P = 0, • • • , n — \...

of the Dissertation On the moduli space of quintic surfaces