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Breathers on a background: periodic and quasiperiodic solutions of extended discrete nonlinear wave systems
Discrete nonlinear wave equation the discrete sine Gordon a discrete nonlinear schrodinger equation the periodic oscillation kink
2014/12/29
In this paper we investigate the emergence of time-periodic and time quasiperiodic (sometimes infinitely long-lived and sometimes very long-lived or metastable) solutions of discrete nonlinear wave eq...
On some classes of mKdV periodic solutions
Vries mKdV equations show that the dynamic stability of the lattice the numerical simulation of the lattice to breathe
2014/12/29
We obtain exact periodic solutions of the positive and negative modified Kortweg–de Vries (mKdV) equations. We examine the dynamical stability of these solitary wave lattices through direct numerical ...
Linearly coupled Bose-Einstein condensates: From Rabi oscillations and quasiperiodic solutions to oscillating domain walls and spiral waves
Unitary transformation the coupled nonlinear schrodinger equation linear field coupling linear coupling is absent the condensate
2014/12/29
In this paper, an exact unitary transformation is examined that allows for the construction of solutions of coupled nonlinear Schrödinger equations with additional linear field coupling, from sol...
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...
Low regularity solutions to a gently stochastic nonlinear wave equation in nonequilibrium statistical mechanics
System stochastic partial differential equations the nonlinear medium heat transfer and energy
2014/12/29
We consider a system of stochastic partial differential equations modeling heat conduction in a non-linear medium. We show global existence of solutions for the system in Sobolev spaces of low regular...
Exact static solutions for discrete ϕ4 models free of the Peierls-Nabarro barrier: Discretized first-integral approach
Discrete klein Gordon model the complete solution static static klein Gordon
2014/12/25
We propose a generalization of the discrete Klein-Gordon models free of the Peierls-Nabarro barrier derived in Spreight [Nonlinearity 12, 1373 (1999)] and Barashenkov et al. [Phys. Rev. E 72, 035602(R...
Exact static solutions to a translationally invariant discrete phi4 model
Discrete phi4 models law of conservation of momentum the discrete model
2014/12/25
For a discrete, translationally invariant phi4 model introduced by Barashenkov et al (2005 Phys. Rev. E 72 35602R), we provide the momentum conservation law and demonstrate how the first integral of t...
Counting solutions to binomial complete intersections
Affine systems algebraically closed field characteristics of zero
2014/12/25
We study the problem of counting the total number of affine solutions of a system of n binomials in n variables over an algebraically closed field of characteristic zero. We show that we may decide in...
The higher-dimensional Ablowitz-Ladik model: from (non-)integrability and solitary waves to surprising collapse properties and more exotic solutions
Two-dimensional nonlinear model of discretization solitary wave
2014/12/24
We propose a consideration of the properties of the two-dimensional Ablowitz-Ladik discretization of the ubiquitous nonlinear Schr¨odinger (NLS) model. We use singularity confinement techniques to sug...
Vortex solutions of the discrete Gross-Pitaevskii equation starting from the anti-continuum limit
Dark vortex dynamic evolution two-dimensional discrete nonlinear schrodinger defocused model
2014/12/24
In this paper, we consider the existence, stability and dynamical evolution of dark vortex states in the two-dimensional defocusing discrete nonlinear Schrödinger model, a model of interest both ...
Investigating the relationship between biodiversity and ecosystem multifunctionality: Challenges and solutions
Investigating relationship between biodiversity ecosystem multifunctionality Challenges solutions
2013/6/14
Extensive research shows that more species-rich assemblages are generally more productive and efficient in resource use than comparable assemblages with fewer species. But the question of how diversit...
Strictly stationary solutions of multivariate ARMA equations with i.i.d. noise
Strictly stationary solutions multivariate ARMA equations i.i.d. noise
2011/6/17
We obtain necessary and sufficient conditions for the existence of strictly stationary
solutions of multivariate ARMA equations with independent and identically
distributed noise. For general ARMA(p...
Introducing Monte Carlo Methods with R Solutions to Odd-Numbered Exercises
Monte Carlo Methods R Solutions Odd-Numbered Exercises
2010/3/9
This partial solution manual to our book Introducing Monte Carlo Methods
with R, published by Springer Verlag in the User R! series, on December 2009,
has been compiled both from our own solutions a...
Sur les solutions faibles d'equations differentielles stochastiques
solutions faibles d'equations stochastiques
2009/9/23
Sur les solutions faibles d'equations differentielles stochastiques。
Explicit solutions of moment problems, I。