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Discretization effects in the nonlinear Schrödinger equation
2003
Applied Numerical Mathematics
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Discretization effects in perturbed 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. ...
doi:10.1016/s0168-9274(02)00112-5
fatcat:kfhsxdmzbzcaxastuajkzmdbdq
Optimizing Higher-order Lagrangian Perturbation Theory for Cold Dark Matter Models
[article]
1995
arXiv
pre-print
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We report on the performance of Lagrangian perturbation 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. ...
arXiv:astro-ph/9512106v1
fatcat:fl6tu4jihbbhzc47ztm65rbkle
Nonlinear waves in integrable and nonintegrable systems (Mathematical Modeling and Computation 16) By Jianke Yang
2015
Bulletin of the London Mathematical Society
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The third chapter is an extension of the integrability 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. ...
doi:10.1112/blms/bdu100
fatcat:ryukenp735b6zmx5edlx2kssim
Perturbation theory of optical resonances of deformed dielectric spheres
[article]
2019
arXiv
pre-print
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We find analytical formulas, valid within certain limits, 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. ...
arXiv:1809.02640v2
fatcat:dbxrvxkzpbh3zhkopblwezywty
Weakly nonlinear wavepackets in the Korteweg–de Vries equation: the KdV/NLS connection
2001
Mathematics and Computers in Simulation
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The multiple scales/nonlinear perturbation 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 ...
doi:10.1016/s0378-4754(00)00291-3
fatcat:mhgxwddklvcvbomss5txfbqvye
Simulations of thermal Bose fields in the classical limit
2002
Physical Review A. Atomic, Molecular, and Optical Physics
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We find that this equation will evolve randomised initial wave functions to equilibrium, and compare our numerical data to the predictions of 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. ...
doi:10.1103/physreva.66.053618
fatcat:4wfuw7j5jnfr5ddweud2ah23tm
Semi-empirical determination of the nuclear quadrupole moment of $$^{109}$$Sn
2021
The European Physical Journal Plus
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Contributions from the 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. ...
doi:10.1140/epjp/s13360-021-01231-3
fatcat:qj2u6onhmzfqtj4bu7rcoa34am
Intrinsic nonlinear conductivity induced by the quantum metric dipole
[article]
2022
arXiv
pre-print
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The nonlinear current to 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 . ...
arXiv:2207.02178v1
fatcat:ktasbayxl5c5dabui2ospxp3sy
On enhanced corrections from quasi-degenerate states to heavy quarkonium observables
2016
Physics Letters B
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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. ...
doi:10.1016/j.physletb.2016.08.026
fatcat:itosshiggvfktkvfuux7ko4efu
Perturbation theory of optical resonances of deformed dielectric spheres
2019
Physical Review A
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We find analytical formulas, valid within certain limits, 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. ...
doi:10.1103/physreva.100.023837
fatcat:3lww6bzdi5a5hoedqujjhvvmuu
Inflationary Prediction for Primordial Non-Gaussianity
2005
Physical Review Letters
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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] ). ...
doi:10.1103/physrevlett.95.121302
pmid:16197063
fatcat:qpisvxqb2nar3jrcsydktjwva4
3D Short-Range Wetting and Nonlocality
2008
Physical Review Letters
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This has 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] . ...
doi:10.1103/physrevlett.100.136105
pmid:18517973
fatcat:navytbgfkfajzmduaf6yypcbd4
fNL−gNL mixing in the matter density field at higher orders
2018
Journal of Cosmology and Astroparticle Physics
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In essence, mathematically the equations 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 . ...
doi:10.1088/1475-7516/2018/06/016
fatcat:smwzm4oxwzd6xotke7mipikm3a
Acoustic spectra of a gas-filled rotating spheroid
2020
European journal of mechanics. B, Fluids
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2020 pre-print arXiv:2011.09267v1 fatcat:w7mn3gb2yrefvjnjdutz4cyb2q
Our results pave the way 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- ...
doi:10.1016/j.euromechflu.2020.03.003
fatcat:hjiyhjyns5bufdkh2mib3b4mwu
Asymmetries in production of He+(n=2)with an intense few-cycle attosecond pulse
2013
Physical Review A. Atomic, Molecular, and Optical Physics
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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 ). ...
doi:10.1103/physreva.88.011401
fatcat:o7jz7n22avcl7evoacsd266boy
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