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Discretization effects in the nonlinear Schrödinger equation

Gadi Fibich, Boaz Ilan
2003 Applied Numerical Mathematics  
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]

A.G. Weiss, S. Gottloeber, T. Buchert
1995 arXiv   pre-print
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

Karima Khusnutdinova
2015 Bulletin of the London Mathematical Society  
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]

Andrea Aiello, Jack G. E. Harris, Florian Marquardt
2019 arXiv   pre-print
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

John P. Boyd, Guan-Yu Chen
2001 Mathematics and Computers in Simulation  
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

M. J. Davis, S. A. Morgan, K. Burnett
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 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

M. Elantkowska, J. Ruczkowski, S. Wilman, M. Suski
2021 The European Physical Journal Plus  
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]

Shibalik Lahiri, Kamal Das, Dimitrie Culcer, Amit Agarwal
2022 arXiv   pre-print
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

Y. Kiyo, G. Mishima, Y. Sumino
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.  ... 
doi:10.1016/j.physletb.2016.08.026 fatcat:itosshiggvfktkvfuux7ko4efu

Perturbation theory of optical resonances of deformed dielectric spheres

Andrea Aiello, Jack G. E. Harris, Florian Marquardt
2019 Physical Review A  
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

David H. Lyth, Yeinzon Rodríguez
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] ).  ... 
doi:10.1103/physrevlett.95.121302 pmid:16197063 fatcat:qpisvxqb2nar3jrcsydktjwva4

3D Short-Range Wetting and Nonlocality

A. O. Parry, C. Rascón, N. R. Bernardino, J. M. Romero-Enrique
2008 Physical Review Letters  
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

Hedda A. Gressel, Marco Bruni
2018 Journal of Cosmology and Astroparticle Physics  
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

Sylvie Su, David Cébron, Henri-Claude Nataf, Philippe Cardin, Jérémie Vidal, Max Solazzo, Yann Do
2020 European journal of mechanics. B, Fluids  
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

J. M. Ngoko Djiokap, S. X. Hu, Wei-Chao Jiang, Liang-You Peng, Anthony F. Starace
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 ).  ... 
doi:10.1103/physreva.88.011401 fatcat:o7jz7n22avcl7evoacsd266boy
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