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Journal articles on the topic 'Equations de Schrödinger-Maxwell'

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Published: 4 June 2021
Last updated: 8 February 2022

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1

Zhdanov, Renat, and Maxim Lutfullin. "On separable Schrödinger–Maxwell equations." Journal of Mathematical Physics 39, no. 12 (December 1998): 6454–58. http://dx.doi.org/10.1063/1.532659.

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2

Benci, Vieri, and Donato Fortunato. "Solitons in Schrödinger-Maxwell equations." Journal of Fixed Point Theory and Applications 15, no. 1 (March 2014): 101–32. http://dx.doi.org/10.1007/s11784-014-0184-1.

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3

Ahmed, I., and E. Li. "Simulation of Plasmonics Nanodevices with Coupled Maxwell and Schrödinger Equations using the FDTD Method." Advanced Electromagnetics 1, no. 1 (September 2, 2012): 76. http://dx.doi.org/10.7716/aem.v1i1.40.

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Maxwell and Schrödinger equations are coupled to incorporate quantum effects for the simulation of plasmonics nanodevices. Maxwell equations with Lorentz-Drude (LD) dispersive model are applied to large size plasmonics components, whereas coupled Maxwell and Schrödinger equations are applied to components where quantum effects are needed. The finite difference time domain method (FDTD) is applied to simulate these coupled equations.
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4

D'Aprile, Teresa, and Dimitri Mugnai. "Solitary waves for nonlinear Klein–Gordon–Maxwell and Schrödinger–Maxwell equations." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 134, no. 5 (October 2004): 893–906. http://dx.doi.org/10.1017/s030821050000353x.

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In this paper we study the existence of radially symmetric solitary waves for nonlinear Klein–Gordon equations and nonlinear Schrödinger equations coupled with Maxwell equations. The method relies on a variational approach and the solutions are obtained as mountain-pass critical points for the associated energy functional.
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5

Boccardo, Lucio, and Luigi Orsina. "A semilinear system of Schrödinger–Maxwell equations." Nonlinear Analysis 194 (May 2020): 111453. http://dx.doi.org/10.1016/j.na.2019.02.007.

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6

Umurzhakhova, Zh B., M. D. Koshanova, Zh Pashen, and K. R. Yesmakhanova. "QUASICLASSICAL LIMIT OF THE SCHRÖDINGER-MAXWELL- BLOCH EQUATIONS." PHYSICO-MATHEMATICAL SERIES 2, no. 336 (April 15, 2021): 179–84. http://dx.doi.org/10.32014/2021.2518-1726.39.

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The study of integrable equations is one of the most important aspects of modern mathematical and theoretical physics. Currently, there are a large number of nonlinear integrable equations that have a physical application. The concept of nonlinear integrable equations is closely related to solitons. An object being in a nonlinear medium that maintains its shape at moving, as well as when interacting with its own kind, is called a soliton or a solitary wave. In many physical processes, nonlinearity is closely related to the concept of dispersion. Soliton solutions have dispersionless properties. Connection with the fact that the nonlinear component of the equation compensates for the dispersion term. In addition to integrable nonlinear differential equations, there is also an important class of integrable partial differential equations (PDEs), so-called the integrable equations of hydrodynamic type or dispersionless (quasiclassical) equations [1-13]. Nonlinear dispersionless equations arise as a dispersionless (quasiclassical) limit of known integrable equations. In recent years, the study of dispersionless systems has become of great importance, since they arise as a result of the analysis of various problems, such as physics, mathematics, and applied mathematics, from the theory of quantum fields and strings to the theory of conformal mappings on the complex plane. Well-known classical methods of the theory of intrinsic systems are used to study dispersionless equations. In this paper, we present the quasicalassical limit of the system of (1+1)-dimensional Schrödinger-Maxwell- Bloch (NLS-MB) equations. The system of the NLS-MB equations is one of the classic examples of the theory of nonlinear integrable equations. The NLS-MB equations describe the propagation of optical solitons in fibers with resonance and doped with erbium. And we will also show the integrability of the quasiclassical limit of the NLS-MB using the obtained Lax representation.
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7

Benci, Vieri, and Donato Fortunato. "An eigenvalue problem for the Schrödinger-Maxwell equations." Topological Methods in Nonlinear Analysis 11, no. 2 (June 1, 1998): 283. http://dx.doi.org/10.12775/tmna.1998.019.

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8

Xu, Jiafa, Zhongli Wei, Donal O'Regan, and Yujun Cui. "INFINITELY MANY SOLUTIONS FOR FRACTIONAL SCHRÖDINGER-MAXWELL EQUATIONS." Journal of Applied Analysis & Computation 9, no. 3 (2019): 1165–82. http://dx.doi.org/10.11948/2156-907x.20190022.

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9

Huang, Wen-nian, and X. H. Tang. "Semiclassical solutions for the nonlinear Schrödinger–Maxwell equations." Journal of Mathematical Analysis and Applications 415, no. 2 (July 2014): 791–802. http://dx.doi.org/10.1016/j.jmaa.2014.02.015.

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10

Kim, Jae-Myoung, and Jung-Hyun Bae. "Infinitely many solutions of fractional Schrödinger–Maxwell equations." Journal of Mathematical Physics 62, no. 3 (March 1, 2021): 031508. http://dx.doi.org/10.1063/5.0028800.

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11

Boccardo, Lucio, and Luigi Orsina. "Regularizing effect for a system of Schrödinger–Maxwell equations." Advances in Calculus of Variations 11, no. 1 (January 1, 2018): 75–87. http://dx.doi.org/10.1515/acv-2016-0006.

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AbstractWe prove some existence results for the following Schrödinger–Maxwell system of elliptic equations:\left\{\begin{aligned} &\displaystyle{-}\div(M(x)\nabla u)+A\varphi|u|^{r-2}u=% f,&&\displaystyle u\in W_{0}^{1,2}(\Omega),\\ &\displaystyle{-}\div(M(x)\nabla\varphi)=|u|^{r},&&\displaystyle\varphi\in W_{% 0}^{1,2}(\Omega).\end{aligned}\right.In particular, we prove the existence of a finite energy solution {(u,\varphi)} if {r>2^{*}} and f does not belong to the “dual space” {L^{\frac{2N}{N+2}}(\Omega)}.
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12

Chen, Shang-Jie, and Chun-Lei Tang. "High energy solutions for the superlinear Schrödinger–Maxwell equations." Nonlinear Analysis: Theory, Methods & Applications 71, no. 10 (November 2009): 4927–34. http://dx.doi.org/10.1016/j.na.2009.03.050.

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13

Romanov, V. G. "Phaseless Inverse Problems for Schrödinger, Helmholtz, and Maxwell Equations." Computational Mathematics and Mathematical Physics 60, no. 6 (June 2020): 1045–62. http://dx.doi.org/10.1134/s0965542520060093.

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14

Nakamitsu, Kuniaki, and Masayoshi Tsutsumi. "The Cauchy problem for the coupled Maxwell–Schrödinger equations." Journal of Mathematical Physics 27, no. 1 (January 1986): 211–16. http://dx.doi.org/10.1063/1.527363.

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15

Huang, Wen-nian, and X. H. Tang. "Ground-State Solutions for Asymptotically Cubic Schrödinger–Maxwell Equations." Mediterranean Journal of Mathematics 13, no. 5 (February 25, 2016): 3469–81. http://dx.doi.org/10.1007/s00009-016-0697-5.

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16

Candela, Anna Maria, and Addolorata Salvatore. "Multiple Solitary Waves for Non-Homogeneous Schrödinger–Maxwell Equations." Mediterranean Journal of Mathematics 3, no. 3-4 (November 2006): 483–93. http://dx.doi.org/10.1007/s00009-006-0092-8.

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17

Azzollini, A., and A. Pomponio. "Ground state solutions for the nonlinear Schrödinger–Maxwell equations." Journal of Mathematical Analysis and Applications 345, no. 1 (September 2008): 90–108. http://dx.doi.org/10.1016/j.jmaa.2008.03.057.

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18

Wada, Takeshi. "Smoothing effects for Schrödinger equations with electro-magnetic potentials and applications to the Maxwell–Schrödinger equations." Journal of Functional Analysis 263, no. 1 (July 2012): 1–24. http://dx.doi.org/10.1016/j.jfa.2012.04.010.

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19

Chen, Shang-Jie, and Chun-Lei Tang. "Multiple solutions for nonhomogeneous Schrödinger–Maxwell and Klein– Gordon–Maxwell equations on R 3." Nonlinear Differential Equations and Applications NoDEA 17, no. 5 (March 31, 2010): 559–74. http://dx.doi.org/10.1007/s00030-010-0068-z.

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20

Xie, Guoda, Zhixiang Huang, Ming Fang, and Wei E. I. Sha. "Simulating Maxwell–Schrödinger Equations by High-Order Symplectic FDTD Algorithm." IEEE Journal on Multiscale and Multiphysics Computational Techniques 4 (2019): 143–51. http://dx.doi.org/10.1109/jmmct.2019.2920101.

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21

RUIZ, DAVID. "SEMICLASSICAL STATES FOR COUPLED SCHRÖDINGER–MAXWELL EQUATIONS: CONCENTRATION AROUND A SPHERE." Mathematical Models and Methods in Applied Sciences 15, no. 01 (January 2005): 141–64. http://dx.doi.org/10.1142/s0218202505003939.

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In this paper we study a coupled nonlinear Schrödinger–Maxwell system of equations. In this framework, we are concerned with the existence of semiclassical states. We use a perturbation scheme in a variational setting in order to study the concentration of the solutions when the Planck constant is supposed to be small enough.
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22

KOUZAEV, GUENNADI A. "HERTZ VECTORS AND THE ELECTROMAGNETIC-QUANTUM EQUATIONS." Modern Physics Letters B 24, no. 20 (August 10, 2010): 2117–29. http://dx.doi.org/10.1142/s0217984910024523.

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In this letter, a new form of electromagnetic-quantum equations is proposed. The electric and magnetic potentials are expressed through a single Hertz vector, and the systems of quantum and Maxwell equations are transformed into more compact integro-differential ones. These new forms are given for the Schrödinger, Pauli, Dirac and Klein–Gordon equations, and a practical way to calculate them by available software tools is considered.
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23

Sun, Juntao. "Infinitely many solutions for a class of sublinear Schrödinger–Maxwell equations." Journal of Mathematical Analysis and Applications 390, no. 2 (June 2012): 514–22. http://dx.doi.org/10.1016/j.jmaa.2012.01.057.

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24

Huang, Wen-nian, and X. H. Tang. "SEMICLASSICAL SOLUTIONS FOR THE NONLINEAR SCHRÖDINGER-MAXWELL EQUATIONS WITH CRITICAL NONLINEARITY." Taiwanese Journal of Mathematics 18, no. 4 (August 2014): 1203–17. http://dx.doi.org/10.11650/tjm.18.2014.3993.

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25

Leopold, Nikolai, and Peter Pickl. "Derivation of the Maxwell--Schrödinger Equations from the Pauli--Fierz Hamiltonian." SIAM Journal on Mathematical Analysis 52, no. 5 (January 2020): 4900–4936. http://dx.doi.org/10.1137/19m1307639.

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26

Shimomura, Akihiro. "Modified Wave Operators for Maxwell-Schrödinger Equations in Three Space Dimensions." Annales Henri Poincaré 4, no. 4 (August 2003): 661–83. http://dx.doi.org/10.1007/s00023-003-0143-7.

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27

Nakamura, Makoto, and Takeshi Wada. "Global Existence and Uniqueness of Solutions to the Maxwell-Schrödinger Equations." Communications in Mathematical Physics 276, no. 2 (September 25, 2007): 315–39. http://dx.doi.org/10.1007/s00220-007-0337-9.

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28

Dai, Wei, Zhao Liu, and Guolin Qin. "Classification of Nonnegative Solutions to Static Schrödinger--Hartree--Maxwell Type Equations." SIAM Journal on Mathematical Analysis 53, no. 2 (January 2021): 1379–410. http://dx.doi.org/10.1137/20m1341908.

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29

BOUCHERES, T., T. COLIN, B. NKONGA, B. TEXIER, and A. BOURGEADE. "STUDY OF A MATHEMATICAL MODEL FOR STIMULATED RAMAN SCATTERING." Mathematical Models and Methods in Applied Sciences 14, no. 02 (February 2004): 217–52. http://dx.doi.org/10.1142/s0218202504003222.

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We study a semiclassical modelization of the interaction of a laser with a mono-atomic gas. The Maxwell equations are coupled with a three-level version of the Bloch equations. Taking into account the specificities of the laser pulse and of the gas, we introduce small parameters and a dimensionless form of the equations. To describe stimulated Raman scattering, we perform a three-scale WKB expansion in the weakly nonlinear regime of geometric optics. The limit system is of Schrödinger–Bloch type. We prove a global existence result for this system and the convergence of its solution toward the solution of the initial Maxwell–Bloch equations, as the parameter of the WKB expansion goes to 0. We put in evidence Raman instability in the one-dimensional case, both theoretically and numerically.
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30

LESCARRET, VINCENT. "INTERMEDIATE MODEL FOR SPATIAL EVOLUTION IN NONLINEAR OPTICS." Mathematical Models and Methods in Applied Sciences 20, no. 08 (August 2010): 1209–49. http://dx.doi.org/10.1142/s0218202510004581.

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This paper follows the work of Colin–Gallice–Laurioux6in which a new model generalizing the Schrödinger (NLS) model of the diffractive optics is derived for the laser propagation in nonlinear media. In particular, it provides good approximate solutions of the Maxwell–Lorentz system for highly oscillating initial data with broad spectrum. In real situations one is given boundary data. We propose to derive a similar evolution model but in the variable associated to the direction of propagation. However, since the space directions for the Maxwell equations are not hyperbolic, the boundary problem is ill-posed and one needs to apply a cutoff defined in the Fourier space, selecting those frequencies for which the operator is hyperbolic. The model we obtain is nearly L2conservative on its domain of validity.We then give a justification of the derivation. For this purpose we introduce a related well-posed initial boundary value problem. Finally, we perform numerical computations on the example of Maxwell with Kerr nonlinearity in some cases of short or spectrally chirped data where our model outperforms the Schrödinger one.
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31

Li, Qingdong, Han Su, and Zhongli Wei. "Existence of infinitely many large solutions for the nonlinear Schrödinger–Maxwell equations." Nonlinear Analysis: Theory, Methods & Applications 72, no. 11 (June 2010): 4264–70. http://dx.doi.org/10.1016/j.na.2010.02.002.

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32

Chen, Peng, and Cai Tian. "Infinitely many solutions for Schrödinger–Maxwell equations with indefinite sign subquadratic potentials." Applied Mathematics and Computation 226 (January 2014): 492–502. http://dx.doi.org/10.1016/j.amc.2013.10.069.

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33

Huang, Wen-nian, and X. H. Tang. "The Existence of Infinitely Many Solutions for the Nonlinear Schrödinger–Maxwell Equations." Results in Mathematics 65, no. 1-2 (October 25, 2013): 223–34. http://dx.doi.org/10.1007/s00025-013-0342-6.

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34

Kozlov, V. V. "Linear System of Differential Equations with a Quadratic Invariant as the Schrödinger Equation." Doklady Mathematics 103, no. 1 (January 2021): 39–43. http://dx.doi.org/10.1134/s1064562421010075.

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Abstract Linear systems of differential equations with an invariant in the form of a positive definite quadratic form in a real Hilbert space are considered. It is assumed that the system has a simple spectrum and the eigenvectors form a complete orthonormal system. Under these assumptions, the linear system can be represented in the form of the Schrödinger equation by introducing a suitable complex structure. As an example, we present such a representation for the Maxwell equations without currents. In view of these observations, the dynamics defined by some linear partial differential equations can be treated in terms of the basic principles and methods of quantum mechanics.
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35

Azzollini, A., P. d'Avenia, and A. Pomponio. "On the Schrödinger–Maxwell equations under the effect of a general nonlinear term." Annales de l'Institut Henri Poincare (C) Non Linear Analysis 27, no. 2 (March 2010): 779–91. http://dx.doi.org/10.1016/j.anihpc.2009.11.012.

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36

Liu, Zhisu, Shangjiang Guo, and Ziheng Zhang. "EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR A CLASS OF SUBLINEAR SCHRÖDINGER-MAXWELL EQUATIONS." Taiwanese Journal of Mathematics 17, no. 3 (May 2013): 857–72. http://dx.doi.org/10.11650/tjm.17.2013.2202.

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37

BECHOUCHE, PHILIPPE, NORBERT J. MAUSER, and SIGMUND SELBERG. "ON THE ASYMPTOTIC ANALYSIS OF THE DIRAC–MAXWELL SYSTEM IN THE NONRELATIVISTIC LIMIT." Journal of Hyperbolic Differential Equations 02, no. 01 (March 2005): 129–82. http://dx.doi.org/10.1142/s0219891605000415.

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We study the behavior of solutions of the Dirac–Maxwell system (DM) in the nonrelativistic limit c → ∞, where c is the speed of light. DM is a nonlinear system of PDEs obtained by coupling the Dirac equation for a 4-spinor to the Maxwell equations for the self-consistent field created by the moving charge of the spinor. The limit c → ∞, sometimes also called post-Newtonian, yields a Schrödinger–Poisson system, where the spin and magnetic field no longer appear. We prove that DM is locally well-posed for H1 data (for fixed c), and that as c → ∞ the existence time grows at least as fast as log(c), provided the data are uniformly bounded in H1. Moreover, if the datum for the Dirac spinor converges in H1, then the solution of DM converges, modulo a phase correction, in C([0,T];H1) to a solution of a Schrödinger–Poisson system. Our results also apply to a mixed state formulation of DM, and give also a convergence result for the Pauli equation as the "semi-nonrelativistic" limit. The proof relies on modifications of the bilinear null form estimates of Klainerman and Machedon, and extends our previous work on the nonrelativistic limit of the Klein–Gordon–Maxwell system.
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38

Li, Zhi-Qiang, Shou-Fu Tian, Wei-Qi Peng, and Jin-Jie Yang. "Inverse Scattering Transform and Soliton Classification of Higher-Order Nonlinear Schrödinger-Maxwell-Bloch Equations." Theoretical and Mathematical Physics 203, no. 3 (June 2020): 709–25. http://dx.doi.org/10.1134/s004057792006001x.

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39

Chen, Yongpin P., Wei E. I. Sha, Lijun Jiang, Min Meng, Yu Mao Wu, and Weng Cho Chew. "A unified Hamiltonian solution to Maxwell–Schrödinger equations for modeling electromagnetic field–particle interaction." Computer Physics Communications 215 (June 2017): 63–70. http://dx.doi.org/10.1016/j.cpc.2017.02.006.

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40

Liu, Leilei, Weiguo Zhang, and Jian Xu. "On a Riemann–Hilbert problem for the NLS-MB equations." Modern Physics Letters B 35, no. 25 (August 3, 2021): 2150420. http://dx.doi.org/10.1142/s0217984921504200.

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In this paper, we study a coupled system of the nonlinear Schrödinger (NLS) equation and the Maxwell–Bloch (MB) equation with nonzero boundary conditions by Riemann–Hilbert (RH) method. We obtain the formulae of the simple-pole and the multi-pole solutions via a matrix Riemann–Hilbert problem (RHP). The explicit form of the soliton solutions for the NLS-MB equations is obtained. The soliton interaction is also given. Furthermore, we show that the multi-pole solutions can be viewed as some proper limits of the soliton solutions with simple poles, and the multi-pole solutions constitute a novel analytical viewpoint in nonlinear complex phenomena. The advantage of this way is that it avoids solving the complex symmetric relations and repeatedly solving residue conditions.
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41

Bersons, I. "Soliton Model of the Photon / Fotona Solitona Modelis." Latvian Journal of Physics and Technical Sciences 50, no. 2 (April 1, 2013): 60–67. http://dx.doi.org/10.2478/lpts-2013-0013.

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A three-dimensional soliton model of photon with corpuscular and wave properties is proposed. We consider the Maxwell equations and assume that light induces the polarization and magnetization of vacuum only along the direction of its propagation. The nonlinear equation constructed for the vector potential is similar to the generalized nonlinear Schrödinger equation and comprises a dimensionless constant μ that determines the size-scale of soliton and is expected to be small. The obtained one-soliton solution of the proposed nonlinear equation describes a three-dimensional object identified as photon.
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42

Kikuchi, Hiroaki. "On the existence of a solution for elliptic system related to the Maxwell–Schrödinger equations." Nonlinear Analysis: Theory, Methods & Applications 67, no. 5 (September 2007): 1445–56. http://dx.doi.org/10.1016/j.na.2006.07.029.

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43

Avetisyan, Yu A., and E. D. Trifonov. "Maxwell-Schrödinger equations for a dilute gas Bose-Einstein condensate coupled to an electromagnetic field." Journal of Experimental and Theoretical Physics 106, no. 3 (March 2008): 426–34. http://dx.doi.org/10.1134/s1063776108030023.

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44

ANDREEV, PAVEL A. "NONINTEGRAL FORM OF THE GROSS–PITAEVSKII EQUATION FOR POLARIZED MOLECULES." Modern Physics Letters B 27, no. 13 (May 10, 2013): 1350096. http://dx.doi.org/10.1142/s0217984913500966.

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The Gross–Pitaevskii equation for polarized molecules is an integro-differential equation, consequently it is complicated for solving. We find a possibility to represent it as a nonintegral nonlinear Schrödinger equation, but this equation should be coupled with two linear equations describing the electric field. These two equations are the Maxwell equations. We recapture the dispersion of collective excitations in the three-dimensional electrically polarized BEC with no evolution of the electric dipole moment directions. We trace the contribution of the electric dipole moment. We explicitly consider the contribution of the electric dipole moment in the interaction constant for the short-range interaction. We show that the spectrum of dipolar BEC does not reveal instability at repulsive short-range interaction. Nonlinear excitations are also considered. We present dependence of the bright soliton characteristics on the electric dipole moment.
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45

SI, LIUGANG, XINYOU LÜ, PEIJUN SONG, and JIBING LIU. "ULTRASLOW SOLITONS VIA FOUR-WAVE MIXING IN A CRYSTAL OF MOLECULAR MAGNETS." Modern Physics Letters B 23, no. 07 (March 20, 2009): 989–1004. http://dx.doi.org/10.1142/s0217984909019181.

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The authors theoretically investigate the formation of ultraslow dark and bright solitons via four-wave mixing (FWM) in a crystal of molecular magnets in the presence of a uniform d.c. magnetic field, where two strong continuous wave pump electromagnetic fields and a weak-pulsed probe electromagnetic field produce a pulsed FWM electromagnetic field. By solving the Maxwell–Schrödinger equations under the slowly varying envelope approximation and rotating-wave approximations, we demonstrate that both the weak-pulsed probe and FWM electromagnetic fields can evolve into dark and bright solitons with the same shape and the same ultraslow group velocity.
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46

Wu, Xiao-Yu, Bo Tian, Hui-Ling Zhen, Wen-Rong Sun, and Ya Sun. "Solitons for the (2+1)-dimensional nonlinear Schrödinger-Maxwell-Bloch equations in an erbium-doped fibre." Journal of Modern Optics 63, no. 6 (October 5, 2015): 590–97. http://dx.doi.org/10.1080/09500340.2015.1086031.

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47

Wang, Lei, Xiao Li, Feng-Hua Qi, and Lu-Lu Zhang. "Breather interactions and higher-order nonautonomous rogue waves for the inhomogeneous nonlinear Schrödinger Maxwell–Bloch equations." Annals of Physics 359 (August 2015): 97–114. http://dx.doi.org/10.1016/j.aop.2015.04.025.

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48

Song, Jiang-Yan, Chi-Ping Zhang, and Yu Xiao. "Determinant representation of Darboux transformation for the (2+1)-dimensional nonlocal nonlinear Schrödinger-Maxwell-Bloch equations." Optik 228 (February 2021): 166150. http://dx.doi.org/10.1016/j.ijleo.2020.166150.

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49

Tsutsumi, Yoshio. "Global existence and asymptotic behavior of solutions for the Maxwell-Schrödinger equations in three space dimensions." Communications in Mathematical Physics 151, no. 3 (February 1993): 543–76. http://dx.doi.org/10.1007/bf02097027.

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50

Porsezian, K., and K. Nakkeeran. "Singularity structure analysis and the complete integrability of the higher order nonlinear Schrödinger-Maxwell-Bloch equations." Chaos, Solitons & Fractals 7, no. 3 (March 1996): 377–82. http://dx.doi.org/10.1016/0960-0779(95)00069-0.

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