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Discretization effects in the nonlinear Schrödinger equation

2003
*
Applied Numerical Mathematics
*

Discretization effects in perturbed

doi:10.1016/s0168-9274(02)00112-5
fatcat:kfhsxdmzbzcaxastuajkzmdbdq
*NLS*equations are also discussed. ... The modified equation of the semi-discrete*NLS*, which is the*NLS*with highorder anisotropic dispersion, captures the arrest of collapse but not the subsequent oscillations. ... Acknowledgements The authors would like to thank Mu Mo*for*pointing out the applicability of their previous work [9] to discretization effects. ...##
###
Optimizing Higher-order Lagrangian Perturbation Theory for Cold Dark Matter Models
[article]

1995
*
arXiv
*
pre-print

We report on the performance of Lagrangian perturbation

arXiv:astro-ph/9512106v1
fatcat:fl6tu4jihbbhzc47ztm65rbkle
*theory*up to the*second**order**for*the standard cold dark matter (SCDM) and broken scale invariance (BSI) scenarios. ... The optimization scheme can be expressed in*a*way which is independent of the type of fluctuation spectrum and of the size of the simulations. ... AGW wishes to thank the AIP in Potsdam*for*the opportunity to work on this project during*a*stay at the AIP. ...##
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Nonlinear waves in integrable and nonintegrable systems (Mathematical Modeling and Computation 16) By Jianke Yang

2015
*
Bulletin of the London Mathematical Society
*

The third chapter is an extension of the integrability

doi:10.1112/blms/bdu100
fatcat:ryukenp735b6zmx5edlx2kssim
*theory**for**a*single*NLS*equation, associated with the*second**order*Zakharov -Shabat spectral problem, to integrable models associated with the higher-*order*... The*second*chapter is devoted to the integrability*theory**for*the*NLS*equation by the Inverse Scattering Transform, the method which was first developed by Gardner, Green, Kruskal and Miura in 1967*for*... Two-wave interactions are shown to be governed by*a**second*-*order*area-preserving map exhibiting*a*fractal structure. ...##
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Perturbation theory of optical resonances of deformed dielectric spheres
[article]

2019
*
arXiv
*
pre-print

We find analytical formulas, valid within certain limits,

arXiv:1809.02640v2
fatcat:dbxrvxkzpbh3zhkopblwezywty
*for*the deformation-induced first- and*second*-*order*corrections to the central frequency and bandwidth of*a*resonance. ... Setting up*a*perturbation series up to*second**order*, we derive both the frequency shifts and modified linewidths. ... This permitted us to develop*a**second*-*order*perturbation*theory**for*the electromagnetic Debye potentials describing the light fields. ...##
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Weakly nonlinear wavepackets in the Korteweg–de Vries equation: the KdV/NLS connection

2001
*
Mathematics and Computers in Simulation
*

The multiple scales/nonlinear perturbation

doi:10.1016/s0378-4754(00)00291-3
fatcat:mhgxwddklvcvbomss5txfbqvye
*theory*is explicitly extended to two*orders*beyond that which yields the*NLS*equation; the wave envelope evolves under*a*Generalized-*NLS*equation which is third ... KdV through perturbation*theory*, resonant effects that give the*NLS*equation*a*wide range of applicability, and numerical illustrations. ... The*NLS*-from-KdV*theory*then has*a*similarly large region of validity. • Our numerical experiments show good agreement between the*NLS*perturbation*theory*and the exact KdV wavepacket*for*small and moderate ...##
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Simulations of thermal Bose fields in the classical limit

2002
*
Physical Review A. Atomic, Molecular, and Optical Physics
*

We find that this equation will evolve randomised initial wave functions to equilibrium, and compare our numerical data to the predictions of

doi:10.1103/physreva.66.053618
fatcat:4wfuw7j5jnfr5ddweud2ah23tm
*a*gapless,*second*-*order**theory*of Bose-Einstein condensation ...*A*. Morgan, J. Phys. B 33, 3847 (2000)]. We find that we can determine the temperature of the equilibrium state when this*theory*is valid. ... Gardiner*for*useful discussions. This work was financially supported by St. John's College and Trinity College, Oxford, and the UK-EPSRC. ...##
###
Semi-empirical determination of the nuclear quadrupole moment of $$^{109}$$Sn

2021
*
The European Physical Journal Plus
*

Contributions from the

doi:10.1140/epjp/s13360-021-01231-3
fatcat:qj2u6onhmzfqtj4bu7rcoa34am
*second*-*order*perturbation*theory*to the electric quadrupole hyperfine structure, concerning spin–orbit correlated hyperfine interactions, were included*for*the first time. ... The contributions from the*second*-*order*perturbation*theory*to the magnetic dipole hyperfine structure, concerning electrostatically correlated hyperfine interactions, were taken into consideration*for*... The parameters*a*01*nl*and*a*12*nl*are modified by the*second*-*order*spin-orbit term. ...##
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Intrinsic nonlinear conductivity induced by the quantum metric dipole
[article]

2022
*
arXiv
*
pre-print

The nonlinear current to

arXiv:2207.02178v1
fatcat:ktasbayxl5c5dabui2ospxp3sy
*second*-*order*in the electric field is known to originate from three different physical mechanisms: extrinsic i) nonlinear Drude and ii) Berry curvature dipole, and intrinsic iii ... The quantum metric dipole induced*NL*Hall current dominates transport in parity-time reversal symmetric systems in the bandgap and near the band edges, something we show explicitly*for*topological antiferromagnets ... Quantum Kinetic*theory*of the*second*-*order*current:-In the quantum kinetic*theory*framework, the*NL*current is calculated via the expression, j*a*= −e m,p v*a*pm ρ (2) mp . ...##
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On enhanced corrections from quasi-degenerate states to heavy quarkonium observables

2016
*
Physics Letters B
*

*For*

*a*heavy quarkonium system, naively, enhanced effects (l-changing mixing effects) could contribute already to the first-

*order*and third-

*order*corrections to the wave function and the energy level, respectively ... It is well known that in perturbation

*theory*existence of quasi-degenerate states can rearrange the

*order*counting. ... Acknowledgements The authors are grateful to Jorge Segovia

*for*bringing their attention to the corrections from quasi-degenerate states. ...

##
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Perturbation theory of optical resonances of deformed dielectric spheres

2019
*
Physical Review A
*

We find analytical formulas, valid within certain limits,

doi:10.1103/physreva.100.023837
fatcat:3lww6bzdi5a5hoedqujjhvvmuu
*for*the deformation-induced first-and*second*-*order*corrections to the central frequency and bandwidth of*a*resonance. ... Setting up*a*perturbation series up to*second**order*, we derive both the frequency shifts and the modified linewidths. ... IV*A**for*details). within first-*order*perturbation*theory*. ...##
###
Inflationary Prediction for Primordial Non-Gaussianity

2005
*
Physical Review Letters
*

*A*formula is given

*for*the normalisation \fnl of the bispectrum of \zeta, which is the main signal of non-gaussianity. ... Examples of the use of the formula are given, and its relation to cosmological perturbation

*theory*is explained. ... In particular, the non-local terms, present at

*second*

*order*

*for*

*a*generic perturbation, must be absent

*for*ζ (see also Ref. [22] ). ...

##
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3D Short-Range Wetting and Nonlocality

2008
*
Physical Review Letters
*

This has

doi:10.1103/physrevlett.100.136105
pmid:18517973
fatcat:navytbgfkfajzmduaf6yypcbd4
*a*simple diagrammatic explanation using*a*nonlocal interfacial Hamiltonian and yields*a*thermodynamically consistent*theory*of wetting in keeping with exact sum rules. ...*For*critical wetting the*second*length serves to lower the cutoff in the spectrum of interfacial fluctuations determining the repulsion from the wall. ... Importantly, the*NL**theory*preserves the Nakanishi-Fisher global phase diagram showing first*order*, critical, and tricritical wetting 136105-3 [10] . ...##
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fNL−gNL mixing in the matter density field at higher orders

2018
*
Journal of Cosmology and Astroparticle Physics
*

In essence, mathematically the equations

doi:10.1088/1475-7516/2018/06/016
fatcat:smwzm4oxwzd6xotke7mipikm3a
*for*the gradient expansion are equivalent to those of first*order*perturbation*theory*, thus first-*order*results convert into gradient expansion results and, vice ... Our analysis is based on the synergy between*a*gradient expansion (aka long-wavelength approximation) and standard perturbation*theory*at higher*order*. ... At fourth*order*, the source terms*for*the particular solution will contain the*second*and third-*order*density contrast and, thus, terms containing both f*NL*and g*NL*. ...##
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Acoustic spectra of a gas-filled rotating spheroid

2020
*
European journal of mechanics. B, Fluids
*

Our results pave the way

doi:10.1016/j.euromechflu.2020.03.003
fatcat:hjiyhjyns5bufdkh2mib3b4mwu
*for*the modal acoustic velocimetry to be*a*robust, versatile, and non-intrusive method*for*mapping large-scale flows. Pages: 1-14 ...*a*large collection of modes. ... Guianvarc"h*for*their interest and encouragements. This work is dedicated to the memory of J. Mehl, who gave the authors his very last en- ...##
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Asymmetries in production of He+(n=2)with an intense few-cycle attosecond pulse

2013
*
Physical Review A. Atomic, Molecular, and Optical Physics
*

*For*most CEPs the asymmetries in the photoelectron angular distributions with excitation of He + (2s) or He + (2p) have opposite signs and are two

*orders*of magnitude larger than

*for*ionization without ... with

*a*carrier frequency of 51 eV. ... From

*a*perturbation

*theory*analysis [16] , the asymmetry P

*nl*(E,ϕ) is proportional to the interference of the first-and

*second*-

*order*amplitudes, i.e., Re(

*A*(1)

*nl*

*A*(2) *

*nl*). ...

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