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Multi-symplectic Runge-Kutta-Nystr鰉 Methods for Nonlinear Schr鰀inger Equations
Nonlinear Schr膐dinger equations multi-symplectic methods Runge-Kutta-Nystr膐mmethods charge conservation law
2012/8/7
In this paper, we investigate multi-symplectic Runge-Kutta-Nystr膐m (RKN) methods for non-
linear Schr膐dinger equations. Concatenating symplecitc Nystr膐m methods in spatial direct...
Conservativity of Symplectic Methods for the Ablowitz-Ladik Discrete Nonlinear Schrodinger Equation
Nonlinear Schrdinger Equation Ablowitz-Ladik Model Darboux
2012/8/7
Using several kinds of Darboux transformations, we standardize the non-
canonical symplectic structure of Ablowitz-Ladik model (A-L model) of the
Nonlinear Schr膐dinger Equation (NLSE), then we emplo...
One Approach to Construction of Bilateral Approximations Methods for Solution of Nonlinear Eigenvalue Problems
Nonlinear Eigenvalue Problem Derivatives of Matrix Determinant Numerical Algorithm of Alternate Approximations
2013/1/30
In this paper a new approach to construction of iterative methods of bilateral approximations of eigenvalue is proposed and investigated. The conditions on initial approximation, which ensure the conv...
Asymptotic behaviour of the doubly nonlinear equation $u_t=Δ_p u^m$ on bounded domains
doubly nonlinear equation slow di usion asymptotic behaviour self-similar solution convergence rates
2012/6/29
We study the homogeneous Dirichlet problem for the doubly nonlinear equation $u_t = \Delta_p u^m$, where $p>1,\ m>0$ posed in a bounded domain in $\mathbb{R}^N$ with homogeneous boundary conditions an...
Some qualitative properties of the solutions of the Magnetohydrodynamic equations for nonlinear bipolar fluids
Non-Newtonian fluids Bipolar fluids Shear thinning fluids MHD Magnetohydrodynamics Asymptotic behavior Long-time behavior Global attractor
2012/6/21
In this article we study the long-time behaviour of a system of nonlinear Partial Differential Equations (PDEs) modelling the motion of incompressible, isothermal and conducting modified bipolar fluid...
A specification test for nonlinear nonstationary models
nonlinear nonstationary models Statistics Theory
2012/6/21
We provide a limit theory for a general class of kernel smoothed U-statistics that may be used for specification testing in time series regression with nonstationary data. The test framework allows fo...
Coupling techniques for nonlinear hyperbolic equations. IV. Multi-component coupling and multidimensional well-balanced schemes
nonlinear hyperbolic equations Multi-component coupling multidimensional well-balanced schemes Analysis of PDEs
2012/6/14
This series of papers is devoted to the formulation and the approximation of coupling problems for nonlinear hyperbolic equations. The coupling across an interface in the physical space is formulated ...
Reflection of Channel-Guided Solitons at Junctions in Two-Dimensional Nonlinear Schroedinger Equation
Reflection of Channel-Guided Solitons Junctions Two-Dimensional Nonlinear Schroedinger Equation Pattern Formation and Solitons
2012/4/26
Solitons confined in channels are studied in the two-dimensional nonlinear Schr\"odinger equation. We study the dynamics of two channel-guided solitons near the junction where two channels are merged....
Empirical Estimators for Stochastically Forced Nonlinear Systems: Observability, Controllability and the Invariant Measure
Empirical Estimators Stochastically Forced Nonlinear Systems Invariant Measure Optimization and Control
2012/4/18
We introduce a data-based approach to estimating key quantities which arise in the study of nonlinear control systems and random nonlinear dynamical systems. Our approach hinges on the observation tha...
Nonlinear dynamo in a short Taylor-Couette setup
Finite elements Magnetohydrodynamics Taylor-Couette dynamo action
2012/4/18
It is numerically demonstrated by means of a magnetohydrodynamics code that a short Taylor-Couette setup with a body force can sustain dynamo action. The magnetic threshold is comparable to what is us...
Continuous dependence for $H^{2}$ critical nonlinear Schr鰀inger equations in high dimensions
Nonlinear Schrodinger equation Continuous dependence Cauchy problem Strichartz抯 estimates
2012/4/17
The global existence of solutions in $H^{2}$ is well known for $H^{2}$ critical nonlinear Schr\"{o}dinger equations with small initial data in high dimensions $d\geq8$. However, even though the soluti...
Continuity of attractors for a nonlinear parabolic problem with terms concentrating in the boundary
Partial differential equations on infinite-dimensional spaces asymptotic behavior of solutions attractors singular perturbations concentrating terms
2012/4/17
We analyze the dynamics of the flow generated by a nonlinear parabolic problem when some reaction and potential terms are concentrated in a neighborhood of the boundary. We assume that this neighborho...
A nonlinear elliptic problem with terms concentrating in the boundary
Semilinear elliptic equations nonlinear boundary conditions singular elliptic equations upper semicontinuity concentrating terms
2012/4/17
In this paper we investigate the behavior of a family of steady state solutions of a nonlinear reaction diffusion equation when some reaction and potential terms are concentrated in a $\epsilon$-neigh...
An Upwind Finite Volume Element Method for Nonlinear Convection Diffusion Problem
Nonlinear Convection-Diffusion Tetrahedron Partition Error Estimates
2013/1/30
A class of upwind finite volume element method based on tetrahedron partition is put forward for a nonlinear convection diffusion problem. Some techniques, such as calculus of variations, commutating ...
Stability of nonlinear stochastic Volterra difference equations with continuous time
Nonlinear stochastic difference equations Stability Lyapunov functional construction Continuous time
2011/11/4
In recent years, many authors investigated the systems of stochastic difference equations with discrete time or the systems of numerical solution for stochastic difference equations with continue time...