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Efficient Estimation of Nonparametric Simultaneous Equations Models
Local Polynomial Regression Nonparametric Additive Models Structural Models Instrumental Variables
2016/1/26
This paper defines a new procedure to efficiently estimate nonparametric simultaneous e-quations models that have been explored by Newey et al (1999) and Su and Ullah (2008).The proposed estimation pr...
Efficient Estimation of Nonparametric Simultaneous Equations Models
Local Polynomial Regression Nonparametric Additive Models Structural Models Instrumental Variables
2016/1/20
This paper defines a new procedure to efficiently estimate nonparametric simultaneous e-quations models that have been explored by Newey et al (1999) and Su and Ullah (2008).The proposed estimation pr...
Algorithm 937: MINRES-QLP for Symmetric and Hermitian Linear Equations and Least-Squares Problems
Symmetric Hermitian Linear
2015/7/3
If the system is singular, MINRES-QLP computes the unique
minimum-length solution (also known as the pseudoinverse solution), which generally eludes MINRES. In
all cases, it overcomes a potential in...
SOLUTION OF SPARSE LINEAR EQUATIONS USING CHOLESKY FACTORS OF AUGMENTED SYSTEMS
sparse linear equations direct methods unsymmetric matrices
2015/7/3
Cholesky factorizations have reached a high peak of e±ciency for solving sparse
symmetric systems, largely because their Analyze and Factor phases do not con°ict. We explore the
possibility of using...
An Excursion from Enumerative Geometry to Solving Systems of Polynomial Equations with Macaulay 2
To solve the polynomial equations mathematics geometry cross theory
2014/12/29
Solving a system of polynomial equations is a ubiquitous problem in the applications of mathematics. Until recently, it has been hopeless to find explicit solutions to such systems, and mathematics ha...
Modulational instability of Gross-Pitaevskii-type equations in 1+1 dimensions
The coupling instability nonlinear schrodinger equation matter waves lens type conversion
2014/12/29
The modulational instability of the nonlinear Schrödinger (NLS) equation is examined in the case with a quadratic external potential. This study is motivated by recent experimental results in the...
Modulational instabilities and domain walls in coupled discrete nonlinear Schrödinger equations
Discrete nonlinear schrodinger equation linear coupling plane wave coupling
2014/12/29
We consider a system of two discrete nonlinear Schrödinger equations, coupled by nonlinear and linear terms. For various physically relevant cases, we derive a modulational instability criterion ...
Solitary wave interactions in dispersive equations using Manton’s approach
Invariant to calculate solitary wave dispersion equation solitary wave vries equation and nonlinear schrodinger equation
2014/12/29
We generalize the approach first proposed by Manton [Nucl. Phys. B 150, 397 (1979)] to compute solitary wave interactions in translationally invariant, dispersive equations that support such localized...
Asymptotic behaviour of small solutions for the discrete nonlinear Schrödinger and Klein–Gordon equations
Discrete schrodinger propagator klein Gordon equation form the analysis of decay estimate
2014/12/29
We show decay estimates for the propagator of the discrete Schrödinger and Klein–Gordon equations in the form {{\| {U(t)f} \|}_{{l^\infty}}} \leq C (1+|t|)^{-d/3}{{\| {f} \|}_{{l^1}}} . This impl...
Discrete nonlinear Schrödinger equations free of the Peierls–Nabarro potential
Discrete nonlinear schrodinger equation nonlinear discrete fixed discrete soliton
2014/12/25
We derive a class of discrete nonlinear Schrödinger (DNLS) equations for general polynomial nonlinearity whose stationary solutions can be found from a reduced two-point algebraic problem. It is ...
On a class of spatial discretizations of equations of the nonlinear Schrödinger type
Discrete nonlinear schrodinger equation nonlinear discrete model and discrete
2014/12/25
We demonstrate the systematic derivation of a class of discretizations of nonlinear Schrödinger (NLS) equations for general polynomial nonlinearity whose stationary solutions can be found from a ...
Emergence of unstable modes in an expanding domain for energy-conserving wave equations
Simulated energy wave equation the nonlinear schrodinger equation the coupling
2014/12/25
Motivated by recent work on instabilities in expanding domains in reaction–diffusion settings, we propose an analog of such mechanisms in energy-conserving wave equations. In particular, we consider a...
SYMMETRY-BREAKING BIFURCATION IN NONLINEAR SCHRODINGER/GROSS-PITAEVSKII EQUATIONS
Nonlinear schrodinger mathematical modeling nonlinear optics macroscopic quantum phenomena the number of particles the mixed pattern
2014/12/25
We consider a class of nonlinear Schrödinger/Gross–Pitaeveskii (NLS-GP) equations, i.e., NLS with a linear potential. NLS-GP plays an important role in the mathematical modeling of nonlinear opti...
Soliton dynamics in linearly coupled discrete nonlinear Schrodinger equations
Soliton dynamics system coupling discrete nonlinear schrodinger equation
2014/12/24
We study soliton dynamics in a system of two linearly coupled discrete nonlinear Schrödinger equations, which describe the dynamics of a two-component Bose gas, coupled by an electromagnetic fiel...
Short pulse equations and localized structures in frequency band gaps of nonlinear metamaterials
Short pulse propagation nonlinear metamaterials nonlinear dielectric short pulse linear electromagnetic waves magnetic permeability
2014/12/24
We consider short pulse propagation in nonlinear metamaterials characterized by a weak Kerr-type nonlinearity in their dielectric response. Two short-pulse equations (SPEs) are derived for the high- a...