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Journal articles on the topic 'Schroedinger nonlineaire'

Author: Grafiati

Published: 4 June 2021

Last updated: 18 February 2022

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1

MAHMOOD, M. F., and S. B. QADRI. "MODELING PROPAGATION OF CHIRPED SOLITONS IN AN ELLIPTICALLY LOW BIREFRINGENT SINGLE-MODE OPTICAL FIBER." Journal of Nonlinear Optical Physics & Materials 08, no. 04 (1999): 469–75. http://dx.doi.org/10.1142/s0218863599000345.

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An analytical description is presented, for the first time, to describe propagation dynamics of chirped solitons in an elliptically low birefringent optical fiber within the framework of a model described by coupled nonlinear Schroedinger equations. Using nonlinear Schroedinger solitons as trial functions in an averaged Lagrangian formulation, a set of ordinary differential equations (ODEs) are derived for various soliton parameters. These ODEs describe chirped soliton dynamics and give a criterion for nonlinear coupling of polarized pulses to form a bound state corresponding to a phase mismat

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2

Benci, Vieri, Marco Ghimenti, and Anna Maria Micheletti. "The nonlinear Schroedinger equation: Solitons dynamics." Journal of Differential Equations 249, no. 12 (2010): 3312–41. http://dx.doi.org/10.1016/j.jde.2010.09.026.

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3

ABLOWITZ, MARK J., and CONSTANCE M. SCHOBER. "HAMILTONIAN INTEGRATORS FOR THE NONLINEAR SCHROEDINGER EQUATION." International Journal of Modern Physics C 05, no. 02 (1994): 397–401. http://dx.doi.org/10.1142/s012918319400057x.

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Hamiltonian integration schemes for the Nonlinear Schroedinger Equation are examined. The efficiency with respect to accuracy and integration time of an integrable scheme, a standard conservative scheme, and a symplectic method is compared.

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4

Mahmood, M. F. "Polarized Chirped Soliton Oscillations in a Lossy Elliptically Low Birefringent Optical Fiber." Zeitschrift für Naturforschung A 55, no. 11-12 (2000): 941–44. http://dx.doi.org/10.1515/zna-2000-11-1220.

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Abstract Using a variational method, a new model of the nonlinear propagation of optical solitons generated from semiconductor lasers through a lossy elliptically low birefringent fiber, is presented within the frame-work of a system of coupled nonlinear Schroedinger (CNLS) equations. This model demonstrates polarized soliton oscillations in a lossy elliptically low birefringent fiber.

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5

Kim, Jong Uhn. "Invariant measures for a stochastic nonlinear Schroedinger equation." Indiana University Mathematics Journal 55, no. 2 (2006): 687–718. http://dx.doi.org/10.1512/iumj.2006.55.2701.

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6

Skibsted, Erik. "Propagation estimates forN-body Schroedinger operators." Communications in Mathematical Physics 142, no. 1 (1991): 67–98. http://dx.doi.org/10.1007/bf02099172.

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7

Degasperis, A., S. V. Manakov, and P. M. Santini. "Multiple-scale perturbation beyond the nonlinear Schroedinger equation. I." Physica D: Nonlinear Phenomena 100, no. 1-2 (1997): 187–211. http://dx.doi.org/10.1016/s0167-2789(96)00179-0.

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8

Plastino, A. R., and C. Tsallis. "Nonlinear Schroedinger equation in the presence of uniform acceleration." Journal of Mathematical Physics 54, no. 4 (2013): 041505. http://dx.doi.org/10.1063/1.4798999.

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9

Hidano, Kunio. "Nonlinear Schroedinger Equations with Radially Symmetric Data of Critical Regularity." Funkcialaj Ekvacioj 51, no. 1 (2008): 135–47. http://dx.doi.org/10.1619/fesi.51.135.

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10

Rasmussen, J. Juul, and K. Rypdal. "Blow-up in Nonlinear Schroedinger Equations-I A General Review." Physica Scripta 33, no. 6 (1986): 481–97. http://dx.doi.org/10.1088/0031-8949/33/6/001.

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11

Jeanjean, Louis, and Kazunaga Tanaka. "A positive solution for a nonlinear Schroedinger equation on R^N." Indiana University Mathematics Journal 54, no. 2 (2005): 443–64. http://dx.doi.org/10.1512/iumj.2005.54.2502.

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12

Duell, Wolf-Patrick, and Guido Schneider. "Justification of the nonlinear Schroedinger equation for a resonant Boussinesq model." Indiana University Mathematics Journal 55, no. 6 (2006): 1813–34. http://dx.doi.org/10.1512/iumj.2006.55.2824.

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13

Bountis, Tassos, and Fernando D. Nobre. "Travelling-wave and separated variable solutions of a nonlinear Schroedinger equation." Journal of Mathematical Physics 57, no. 8 (2016): 082106. http://dx.doi.org/10.1063/1.4960723.

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14

Schrader, D. "Explicit calculation of N-soliton solutions of the nonlinear Schroedinger equation." IEEE Journal of Quantum Electronics 31, no. 12 (1995): 2221–25. http://dx.doi.org/10.1109/3.477750.

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15

Mel'nikov, V. K. "Integration of the nonlinear Schroedinger equation with a self-consistent source." Communications in Mathematical Physics 137, no. 2 (1991): 359–81. http://dx.doi.org/10.1007/bf02431884.

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16

Boffetta, G., and A. R. Osborne. "Computation of the direct scattering transform for the nonlinear Schroedinger equation." Journal of Computational Physics 102, no. 2 (1992): 252–64. http://dx.doi.org/10.1016/0021-9991(92)90370-e.

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17

Fefferman, C. L., and M. I. Weinstein. "Continuum Schroedinger Operators for Sharply Terminated Graphene-Like Structures." Communications in Mathematical Physics 380, no. 2 (2020): 853–945. http://dx.doi.org/10.1007/s00220-020-03868-0.

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18

Meškauskas, T., and F. Ivanauskas. "Initial Boundary-Value Problems for Derivative Nonlinear Schroedinger Equation. Justification of Two-Step Algorithm." Nonlinear Analysis: Modelling and Control 7, no. 2 (2002): 69–104. http://dx.doi.org/10.15388/na.2002.7.2.15195.

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We investigate two different initial boundary-value problems for derivative nonlinear Schrödinger equation. The boundary conditions are Dirichlet or generalized periodic ones. We propose a two-step algorithm for numerical solving of this problem. The method consists of Bäcklund type transformations and difference scheme. We prove the convergence and stability in C and H1 norms of Crank–Nicolson finite difference scheme for the transformed problem. There are no restrictions between space and time grid steps. For the derivative nonlinear Schrödinger equation, the proposed numerical algorithm con

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19

Ayati, Z., J. Biazar, and S. Ebrahimi. "A new homotopy perturbation method for solving linear and nonlinear Schroedinger equations." Journal of Interpolation and Approximation in Scientific Computing 2014 (2014): 1–8. http://dx.doi.org/10.5899/2014/jiasc-00062.

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20

Demoulini, Sophia. "Global existence for a nonlinear Schroedinger–Chern–Simons system on a surface." Annales de l'Institut Henri Poincare (C) Non Linear Analysis 24, no. 2 (2007): 207–25. http://dx.doi.org/10.1016/j.anihpc.2006.01.004.

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21

Osborne, A. R. "The Hyperelliptic Inverse Scattering Transform for the Periodic, Defocusing Nonlinear Schroedinger Equation." Journal of Computational Physics 109, no. 1 (1993): 93–107. http://dx.doi.org/10.1006/jcph.1993.1202.

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22

Zakharov, V. E., E. A. Kuznetsov, and S. L. Musher. "Quasi classical regime of collapse in the three-dimensional nonlinear Schroedinger equation." Physica D: Nonlinear Phenomena 28, no. 1-2 (1987): 221. http://dx.doi.org/10.1016/0167-2789(87)90138-2.

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23

Van, Cao Long. "Propagation of Ultrashort Pulses in Nonlinear Media." Communications in Physics 26, no. 4 (2017): 301. http://dx.doi.org/10.15625/0868-3166/26/4/9184.

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In this paper, a general propagation equation of ultrashort pulses in an arbitrary dispersive nonlinear medium derived in [9] has been used for the case of Kerr media. This equation which is called Generalized Nonlinear Schroedinger Equation usually has very complicated form and looking for its solutions is usually a very difficult task. Theoretical methods reviewed in this paper to solve this equation are effective only for some special cases. As an example we describe the method of developed elliptic Jacobi function expansion and its expended form: F-expansion Method. Several numerical metho

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24

Bruschi, M. "New Cellular Automata associated with the Schroedinger Discrete Spectral Problem." Journal of Nonlinear Mathematical Physics 13, no. 2 (2006): 205–10. http://dx.doi.org/10.2991/jnmp.2006.13.2.5.

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25

Manakov, S. V., and P. Grinevich. "The inverse spectral problem for the two-dimensional Schroedinger operator." Physica D: Nonlinear Phenomena 28, no. 1-2 (1987): 222. http://dx.doi.org/10.1016/0167-2789(87)90143-6.

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26

Dudko, G. M., Yu A. Filimonov, A. A. Galishnikov, R. Marcelli, and S. A. Nikitov. "Nonlinear Schroedinger equation analysis of MSSW pulse propagation in ferrite-dielectric-metal structure." Journal of Magnetism and Magnetic Materials 272-276 (May 2004): 999–1000. http://dx.doi.org/10.1016/j.jmmm.2003.12.673.

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27

Tian, Huiping, Zhonghao Li, and Guosheng Zhou. "Stable propagation of ultrashort optical pulses in modified higher-order nonlinear Schroedinger equation." Optics Communications 205, no. 1-3 (2002): 221–26. http://dx.doi.org/10.1016/s0030-4018(02)01316-0.

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28

Dorlas, T. C. "Orthogonality and completeness of the Bethe Ansatz eigenstates of the nonlinear Schroedinger model." Communications in Mathematical Physics 154, no. 2 (1993): 347–76. http://dx.doi.org/10.1007/bf02097001.

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29

Kamvissis, Spyridon. "Long time behavior for the focusing nonlinear schroedinger equation with real spectral singularities." Communications in Mathematical Physics 180, no. 2 (1996): 325–41. http://dx.doi.org/10.1007/bf02099716.

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30

YU. SAVRASOV, S. "CALCULATED PHONON DISPERSIONS IN NB USING FASTLY CONVERGENT DENSITY FUNCTIONAL PERTURBATION THEORY." International Journal of Modern Physics B 07, no. 01n03 (1993): 197–202. http://dx.doi.org/10.1142/s0217979293000445.

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Density functional linear response approach is developed in the framework of conventional band theory analysis. It is based on the variational solutions of one–electron Schroedinger equations in linear order. Due to incompleteness of the basis sets in band structure calculations large contributions to the standard perturbation theory are shown to exist. These terms disappear only in plane wave pseudopotential calculations. The formulation allows us to avoid the problem of summation over higher–excited states in all cases. The approach in applied to calculate phonon dispersions in Nb and the re

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31

Marshall, Ian, and Michael Semenov-Tian-Shansky. "Poisson Groups and Differential Galois Theory of Schroedinger Equation on the Circle." Communications in Mathematical Physics 284, no. 2 (2008): 537–52. http://dx.doi.org/10.1007/s00220-008-0539-9.

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32

Maintas, Xanthos N., Charilaos E. Tsagkarakis, Fotios K. Diakonos, and Dimitrios J. Frantzeskakis. "Nonlinear Schroedinger Solitons in Massive Yang-Mills Theory and Partial Localization of Dirac Matter." Journal of Modern Physics 03, no. 08 (2012): 637–44. http://dx.doi.org/10.4236/jmp.2012.38087.

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33

Rypdal, K., and J. Juul Rasmussen. "Blow-up in Nonlinear Schroedinger Equations-II Similarity structure of the blow-up singularity." Physica Scripta 33, no. 6 (1986): 498–504. http://dx.doi.org/10.1088/0031-8949/33/6/002.

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34

Abdou, M. A. "New exact travelling wave solutions for the generalized nonlinear Schroedinger equation with a source." Chaos, Solitons & Fractals 38, no. 4 (2008): 949–55. http://dx.doi.org/10.1016/j.chaos.2007.01.027.

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35

Lee, T. D. "A New Approach to Solve the Low-lying States of the Schroedinger Equation." Journal of Statistical Physics 121, no. 5-6 (2005): 1015–71. http://dx.doi.org/10.1007/s10955-005-5476-9.

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36

Nassif, Cláudio, and P. R. Silva. "Anomalous coalescence from a nonlinear Schroedinger equation with a quintic term: interpretation through Thompson's approach." Physica A: Statistical Mechanics and its Applications 334, no. 3-4 (2004): 335–42. http://dx.doi.org/10.1016/j.physa.2003.11.019.

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37

Mahmood, M. F. "Analytic method for solving coupled nonlinear Schroedinger equations with oscillating terms describing polarized soliton oscillations." Mathematical and Computer Modelling 36, no. 11-13 (2002): 1259–63. http://dx.doi.org/10.1016/s0895-7177(02)00273-x.

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38

Strampp, W., and W. Oevel. "A Nonlinear Derivative Schroedinger-Equation: Its Bi-Hamilton Structures, Their Inverses, Nonlocal Symmetries and Mastersymmetries." Progress of Theoretical Physics 74, no. 4 (1985): 922–25. http://dx.doi.org/10.1143/ptp.74.922.

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39

Azzollini, A., and A. Pomponio. "On the Schroedinger equation in $\mathbb{R}^{N}$ under the effect of a general nonlinear term." Indiana University Mathematics Journal 58, no. 3 (2009): 1361–78. http://dx.doi.org/10.1512/iumj.2009.58.3576.

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40

Sohinger, Vedran. "Bounds on the growth of high Sobolev norms of solutions to nonlinear Schroedinger equations on $\mathbb{R}$." Indiana University Mathematics Journal 60, no. 5 (2011): 1487–516. http://dx.doi.org/10.1512/iumj.2011.60.4399.

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41

Lugiato, L. A., F. Prati, M. L. Gorodetsky, and T. J. Kippenberg. "From the Lugiato–Lefever equation to microresonator-based soliton Kerr frequency combs." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2135 (2018): 20180113. http://dx.doi.org/10.1098/rsta.2018.0113.

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The model, that is usually called the Lugiato–Lefever equation (LLE), was introduced in 1987 with the aim of providing a paradigm for dissipative structure and pattern formation in nonlinear optics. This model, describing a driven, detuned and damped nonlinear Schroedinger equation, gives rise to dissipative spatial and temporal solitons. Recently, the rather idealized conditions, assumed in the LLE, have materialized in the form of continuous wave driven optical microresonators, with the discovery of temporal dissipative Kerr solitons (DKS). These experiments have revealed that the LLE is a p

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42

Benci, Vieri, Carlo R. Grisanti, and Anna Maria Micheletti. "Existence and non existence of the ground state solution for the nonlinear Schroedinger equations with $V(\infty)=0$." Topological Methods in Nonlinear Analysis 26, no. 2 (2005): 203. http://dx.doi.org/10.12775/tmna.2005.031.

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43

Serkin, Vladimir N., E. M. Schmidt, T. L. Belyaeva, E. Marti-Panameno, and H. Salazar. "Femtosecond Maxwellian solitons. II. Verification of a model of the nonlinear Schroedinger equation in the theory of optical solitons." Quantum Electronics 27, no. 11 (1997): 940–43. http://dx.doi.org/10.1070/qe1997v027n11abeh001123.

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44

Nakamura, Akira. "Jacobi Structures of theN-Soliton Solutions of the Nonlinear Schroedinger, the Heisenberg Spin and the Cylindrical Heisenberg Spin Equations." Journal of the Physical Society of Japan 58, no. 12 (1989): 4334–43. http://dx.doi.org/10.1143/jpsj.58.4334.

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45

ONOFRI, E. "SPLITTING LANDAU LEVELS ON THE 2D TORUS BY PERIODIC PERTURBATIONS." International Journal of Modern Physics C 19, no. 11 (2008): 1753–61. http://dx.doi.org/10.1142/s0129183108013266.

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We study the spectrum of the Schroedinger operator for a particle constrained on a two-dimensional flat torus under the combined action of a transverse magnetic field and a conservative force. A numerical method is presented which allows to compute the spectrum with high accuracy. The method employs a fast Fourier transform to accurately represent the momentum variables and takes into account the twisted boundary conditions required by the presence of the magnetic field. An accuracy of 12 digits is attained even with coarse grids. Landau levels are reproduced in the case of a uniform magnetic

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46

DELL'ANTONIO, GIANFAUSTO. "TOWARDS A THEORY OF DECOHERENCE." International Journal of Modern Physics B 18, no. 04n05 (2004): 643–54. http://dx.doi.org/10.1142/s0217979204024264.

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Consider a quantum particle of mass M in R3, described at time 0 by a wave function ϕ(x) with dispersion Δ, interacting independently with a collection of N particles of mass m. Using only Schroedinger's Quantum Mechanics we prove that when N becomes large and m/M becomes small, and if the information at time t>0 about the N particles of small mass in negleted, the system admits a "classical" description, i.e. a description in which the coherence of the wave function over distances of the order of mM-1N-1Δ have disappeared. We consider this a first step towards proving that most "sufficient

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47

Stumpf, H. "Why Quarks are Different from Leptons – An Explanation by a Fermionic Substructure of Leptons and Quarks." Zeitschrift für Naturforschung A 59, no. 11 (2004): 750–64. http://dx.doi.org/10.1515/zna-2004-1104.

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To explain the difference between leptons and quarks, it is assumed that electroweak gauge bosons, leptons and quarks are composites of elementary fermionic constituents denoted by partons (not to be identified with quarks) or subfermions, respectively. The dynamical law of these constituents is assumed to be given by a relativistically invariant nonlinear spinor field theory with local interaction, canonical quantization, selfregularization and probability interpretation. According to the general requirements of field operator algebraic theory, this model is formulated in algebraic Schroeding

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48

Boyd, John P. "Pseudospectral/Delves–Freeman Computations of the Radiation Coefficient for Weakly Nonlocal Solitary Waves of the Third-Order Nonlinear Schroedinger Equation and Their Relation to Hyperasymptotic Perturbation Theory." Journal of Computational Physics 138, no. 2 (1997): 665–94. http://dx.doi.org/10.1006/jcph.1997.5840.

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49

Doebner, H. D. "On Global and Nonlinear Symmetries in Quantum Mechanics." Acta Polytechnica 50, no. 3 (2010). http://dx.doi.org/10.14311/1201.

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50

Fendzi-Donfack, Emmanuel, Jean Pierre Nguenang, and Laurent Nana. "Fractional analysis for nonlinear electrical transmission line and nonlinear Schroedinger equations with incomplete sub-equation." European Physical Journal Plus 133, no. 2 (2018). http://dx.doi.org/10.1140/epjp/i2018-11851-1.

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