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Journal articles on the topic 'Zakharov system'

Author: Grafiati

Published: 4 June 2021

Last updated: 22 February 2023

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1

Bourgain, Jean. "Zakharov system." Duke Mathematical Journal 76, no. 1 (1994): 175–202. http://dx.doi.org/10.1215/s0012-7094-94-07607-2.

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2

Khalique, Chaudry Masood. "Exact Explicit Solutions and Conservation Laws for a Coupled Zakharov-Kuznetsov System." Mathematical Problems in Engineering 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/461327.

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We study a coupled Zakharov-Kuznetsov system, which is an extension of a coupled Korteweg-de Vries system in the sense of the Zakharov-Kuznetsov equation. Firstly, we obtain some exact solutions of the coupled Zakharov-Kuznetsov system using the simplest equation method. Secondly, the conservation laws for the coupled Zakharov-Kuznetsov system will be constructed by using the multiplier approach.

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3

Shcherbina, A. S. "The Singular Limit of the Dissipative Zakharov System." Zurnal matematiceskoj fiziki, analiza, geometrii 11, no. 1 (2015): 75–99. http://dx.doi.org/10.15407/mag11.01.075.

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4

Goubet, O., and I. Moise. "Attractor for dissipative Zakharov system." Nonlinear Analysis: Theory, Methods & Applications 31, no. 7 (1998): 823–47. http://dx.doi.org/10.1016/s0362-546x(97)00441-0.

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5

Linares*, F., G. Ponce**, and J.-C. Saut. "On a Degenerate Zakharov System." Bulletin of the Brazilian Mathematical Society, New Series 36, no. 1 (2005): 1–23. http://dx.doi.org/10.1007/s00574-005-0025-3.

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6

Fang, Yung-Fu, Hsi-Wei Shih, and Kuan-Hsiang Wang. "Local well-posedness for the quantum Zakharov system in one spatial dimension." Journal of Hyperbolic Differential Equations 14, no. 01 (2017): 157–92. http://dx.doi.org/10.1142/s0219891617500059.

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We consider the quantum Zakharov system in one spatial dimension and establish a local well-posedness theory when the initial data of the electric field and the deviation of the ion density lie in a Sobolev space with suitable regularity. As the quantum parameter approaches zero, we formally recover a classical result by Ginibre, Tsutsumi, and Velo. We also improve their result concerning the Zakharov system and a result by Jiang, Lin, and Shao concerning the quantum Zakharov system.

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7

Al-Askar, Farah M., Wael W. Mohammed, Mohammad Alshammari, and M. El-Morshedy. "Effects of the Wiener Process on the Solutions of the Stochastic Fractional Zakharov System." Mathematics 10, no. 7 (2022): 1194. http://dx.doi.org/10.3390/math10071194.

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We consider in this article the stochastic fractional Zakharov system derived by the multiplicative Wiener process in the Stratonovich sense. We utilize two distinct methods, the Riccati–Bernoulli sub-ODE method and Jacobi elliptic function method, to obtain new rational, trigonometric, hyperbolic, and elliptic stochastic solutions. The acquired solutions are helpful in explaining certain fascinating physical phenomena due to the importance of the Zakharov system in the theory of turbulence for plasma waves. In order to show the influence of the multiplicative Wiener process on the exact solut

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8

Li, Rui, Xing Lin, Zongwei Ma, and Jingjun Zhang. "Existence and Uniqueness of Solutions for a Type of Generalized Zakharov System." Journal of Applied Mathematics 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/193589.

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We study the Cauchy problem for a type of generalized Zakharov system. With the help of energy conservation and approximate argument, we obtain global existence and uniqueness in Sobolev spaces for this system. Particularly, this result implies the existence of classical solution for this generalized Zakharov system.

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9

Kato, Isao. "Local well-posedness for the quantum Zakharov system in three and higher dimensions." Journal of Hyperbolic Differential Equations 18, no. 02 (2021): 257–70. http://dx.doi.org/10.1142/s0219891621500077.

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We study the Cauchy problem associated with a quantum Zakharov-type system in three and higher spatial dimensions.Taking the quantum parameter to unit and developing Fourier restriction norm arguments, we establish local well-posedness property for wider range than the one known for the Zakharov system.

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10

Glushanovsky, A. V., M. V. Levner, and N. E. Kalenov. "Alexander G. Zakharov – the first directorof the RAS Library for Natural Sciences. On the occasion of his 100th anniversary." Scientific and Technical Libraries 1, no. 2 (2021): 129–40. http://dx.doi.org/10.33186/1027-3689-2021-2-129-140.

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The article is dedicated to the memory of the first director of the Library of Natural Sciences of the Russian Academy of Sciences (before 1991, the USSR Academy of Sciences). The Library for Natural Sciences was established in 1973 on the basis of the Sector for Special Libraries (in charge of collection development of Moscow research institutes and of their union catalog maintenance). The Library for Natural Sciences was conceived as an information library center focused on science and research information support based on modern technologies. Alexander Grigorievich Zakharov, newly-retired m

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11

Shao, Shuanglin, Chi-Kun Lin, and Jin-Cheng Jiang. "On one dimensional quantum Zakharov system." Discrete and Continuous Dynamical Systems 36, no. 10 (2016): 5445–75. http://dx.doi.org/10.3934/dcds.2016040.

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12

Ozawa, Tohru, and Kenta Tomioka. "Zakharov system in two space dimensions." Nonlinear Analysis 214 (January 2022): 112532. http://dx.doi.org/10.1016/j.na.2021.112532.

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13

GINIBRE, J., and G. VELO. "Scattering theory for the Zakharov system." Hokkaido Mathematical Journal 35, no. 4 (2006): 865–92. http://dx.doi.org/10.14492/hokmj/1285766433.

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14

Jian, Wang. "Multisymplectic Integrator of the Zakharov System." Chinese Physics Letters 25, no. 10 (2008): 3531–34. http://dx.doi.org/10.1088/0256-307x/25/10/004.

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15

Flahaut, I. "Attractors for the dissipative Zakharov system." Nonlinear Analysis: Theory, Methods & Applications 16, no. 7-8 (1991): 599–633. http://dx.doi.org/10.1016/0362-546x(91)90170-6.

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16

Chebotarev, Sergey A., and Valentina A. Sazonova. "Aesthetic aspects of Mark Zakharov’s direction." Neophilology, no. 28 (2021): 726–34. http://dx.doi.org/10.20310/2587-6953-2021-7-28-726-734.

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We present an analysis of the basic aesthetic principles of Mark Zakharov’s directing. We consider the creative path of the director, factors influencing the development of his directorial views and worldview. Throughout his career, Zakharov improved and was constantly on the loo-kout. The director formulated some principles of working with actors. Among them is the need to help an actor, directing him in the right direction of his plan, without turning him into a pawn for directorial experiments. A modern actor must constantly take into account three important theatrical elements: the materia

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17

Yu Bai and Shengfan Zhou. "RANDOM ATTRACTOR OF STOCHASTIC ZAKHAROV LATTICE SYSTEM." Journal of Applied Analysis & Computation 1, no. 2 (2011): 155–71. http://dx.doi.org/10.11948/2011010.

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18

PECHER, Hartmut. "Well-posedness for a modified Zakharov system." Hokkaido Mathematical Journal 36, no. 3 (2007): 467–506. http://dx.doi.org/10.14492/hokmj/1277472864.

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19

Bejenaru, I., S. Herr, J. Holmer, and D. Tataru. "On the 2D Zakharov system withL2Schrödinger data." Nonlinearity 22, no. 5 (2009): 1063–89. http://dx.doi.org/10.1088/0951-7715/22/5/007.

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20

Pava, Jaime Angulo, and Carlos Banquet Brango. "Orbital stability for the periodic Zakharov system." Nonlinearity 24, no. 10 (2011): 2913–32. http://dx.doi.org/10.1088/0951-7715/24/10/013.

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21

Tuluce Demiray, Seyma, and Hasan Bulut. "Some exact solutions of generalized Zakharov system." Waves in Random and Complex Media 25, no. 1 (2014): 75–90. http://dx.doi.org/10.1080/17455030.2014.966798.

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22

Bao, Weizhu, Fangfang Sun, and G. W. Wei. "Numerical methods for the generalized Zakharov system." Journal of Computational Physics 190, no. 1 (2003): 201–28. http://dx.doi.org/10.1016/s0021-9991(03)00271-7.

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23

Khabibullin, I. T. "Discrete Zakharov-Shabat system and integrable equations." Journal of Soviet Mathematics 40, no. 1 (1988): 108–15. http://dx.doi.org/10.1007/bf01084942.

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24

Newton, Paul K. "Wave interactions in the singular Zakharov system." Journal of Mathematical Physics 32, no. 2 (1991): 431–40. http://dx.doi.org/10.1063/1.529430.

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25

Jin, Shi, Peter A. Markowich, and Chunxiong Zheng. "Numerical simulation of a generalized Zakharov system." Journal of Computational Physics 201, no. 1 (2004): 376–95. http://dx.doi.org/10.1016/j.jcp.2004.06.001.

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26

Dai, Zhengde, and Boling Guo. "Inertial fractal sets for dissipative Zakharov system." Acta Mathematicae Applicatae Sinica 13, no. 3 (1997): 279–88. http://dx.doi.org/10.1007/bf02025883.

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27

Haas, F. "Variational approach for the quantum Zakharov system." Physics of Plasmas 14, no. 4 (2007): 042309. http://dx.doi.org/10.1063/1.2722271.

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28

Wang, Jian. "Multisymplectic numerical method for the Zakharov system." Computer Physics Communications 180, no. 7 (2009): 1063–71. http://dx.doi.org/10.1016/j.cpc.2008.12.028.

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29

Cordero Ceballos, Juan Carlos. "Supersonic limit for the Zakharov–Rubenchik system." Journal of Differential Equations 261, no. 9 (2016): 5260–88. http://dx.doi.org/10.1016/j.jde.2016.07.022.

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30

Pankaj, Ram Dayal, and Chiman Lal. "NUMERICAL ELUCIDATION OF KLEIN-GORDON-ZAKHAROV SYSTEM." Jnanabha 51, no. 01 (2021): 207–12. http://dx.doi.org/10.58250/jnanabha.2021.51125.

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We solve the numerically of the coupled 1D Klein-Gordon-Zakharov system (KGZ) equations in short) by PetrovGalerkin method, using linear and cubic B-Spline, as trial functions. The midpoint rule will be functional to advance the solution in time. This scheme is stable to Von Neumann stability analysis. Numerical solution is used to think about the accurateness and show the dynamism of the scheme.

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31

Woods, Lorna. "Zakharov v. Russia (Eur. Ct. H.R.)." International Legal Materials 55, no. 2 (2016): 207–66. http://dx.doi.org/10.5305/intelegamate.55.2.0207.

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The European Court of Human Rights (ECtHR) in Zakharov v. Russia held that the Russian system of surveillance constituted a violation of Article 8 of the European Convention on Human Rights (ECHR). This decision is not the first judgment concerning surveillance, but it is of note because it is a Grand Chamber judgment in which the ECtHR drew together strands of its existing case law. It comes at a time when national systems of surveillance are the subject of much scrutiny: further cases are pending before the ECtHR.

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32

Chakravarti, Sudarshan Kumar. "A Mathematical Modelling with Zakharov System for Langmuir Wave in Unmagnetized Plasma." International Journal of Research in Engineering, Science and Management 3, no. 11 (2020): 134–36. http://dx.doi.org/10.47607/ijresm.2020.389.

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In this article we present a discussion and overview of mathematical result of the self-focusing of a Langmuir wave which governs Zakharov system and has studied the self- focusing of a Langmuir wave following by Gaussian distribution. Langmuir wave propagates through uncharged plasma which governed by Zakharov systems. The phenomenon plays a vital role in the Dynamics. We present the article mathematical model with effect of Landou damping. Relativistic mass oscillation and ponderomotive force on electrons of the ionized plasma encouraged the Langmuir wave which resists the self-focusing effe

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33

Urazboev, G. U., A. A. Reyimberganov, and A. K. Babadjanova. "Integration of the Matrix Nonlinear Schr¨odinger Equation with a Source." Bulletin of Irkutsk State University. Series Mathematics 37 (2021): 63–76. http://dx.doi.org/10.26516/1997-7670.2021.37.63.

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This paper is concerned with studying the matrix nonlinear Schr¨odinger equation with a self-consistent source. The source consists of the combination of the eigenfunctions of the corresponding spectral problem for the matrix Zakharov-Shabat system which has not spectral singularities. The theorem about the evolution of the scattering data of a non-self-adjoint matrix Zakharov-Shabat system which potential is a solution of the matrix nonlinear Schr¨odinger equation with the self-consistent source is proved. The obtained results allow us to solve the Cauchy problem for the matrix nonlinear Schr

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34

Kawala, A. M., and H. K. Abdelaziz. "Comparison Between Numerical Methods for Generalized Zakharov system." International Journal of Mathematical Models and Methods in Applied Sciences 15 (December 7, 2021): 215–22. http://dx.doi.org/10.46300/9101.2021.15.28.

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We present two numerical methods to get approximate solutions for generalized Zakharov system GZS. The first one is Legendre collocation method, which assumes an expansion in a series of Legendre polynomials , for the function and its derivatives occurring in the GZS, the expansion coefficients are then determined by reducing the problem to a system of algebraic equations. The second is differential transform method DTM , it is a transformation technique based on the Taylor series expansion. In this method, certain transformation rules are applied to transform the problem into a set of algebra

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35

Jaworski, Marek. "Rayleigh-Ritz procedure for the Zakharov-Shabat system." Physical Review E 56, no. 5 (1997): 6142–46. http://dx.doi.org/10.1103/physreve.56.6142.

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36

Klaus, Martin, and Cornelis van der Mee. "Wave operators for the matrix Zakharov–Shabat system." Journal of Mathematical Physics 51, no. 5 (2010): 053503. http://dx.doi.org/10.1063/1.3377048.

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37

Marklund, Mattias. "Classical and quantum kinetics of the Zakharov system." Physics of Plasmas 12, no. 8 (2005): 082110. http://dx.doi.org/10.1063/1.2012147.

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38

Hong, Qi, Jia-ling Wang, and Yu-Shun Wang. "A local energy-preserving scheme for Zakharov system." Chinese Physics B 27, no. 2 (2018): 020202. http://dx.doi.org/10.1088/1674-1056/27/2/020202.

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39

Beck, Thomas, Fabio Pusateri, Phil Sosoe, and Percy Wong. "On global solutions of a Zakharov type system." Nonlinearity 28, no. 9 (2015): 3419–41. http://dx.doi.org/10.1088/0951-7715/28/9/3419.

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40

Fang, Yung-Fu, Hung-Wen Kuo, Hsi-Wei Shih, and Kuan-Hsiang Wang. "Semi-classical Limit for the Quantum Zakharov System." Taiwanese Journal of Mathematics 23, no. 4 (2019): 925–49. http://dx.doi.org/10.11650/tjm/180806.

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41

Antonelli, Paolo, and Luigi Forcella. "The electrostatic limit for the 3D Zakharov system." Nonlinear Analysis 163 (November 2017): 19–33. http://dx.doi.org/10.1016/j.na.2017.07.004.

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42

Fermo, L., C. van der Mee, and S. Seatzu. "Scattering data computation for the Zakharov-Shabat system." Calcolo 53, no. 3 (2015): 487–520. http://dx.doi.org/10.1007/s10092-015-0159-7.

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43

Hani, Zaher, Fabio Pusateri, and Jalal Shatah. "Scattering for the Zakharov System in 3 Dimensions." Communications in Mathematical Physics 322, no. 3 (2013): 731–53. http://dx.doi.org/10.1007/s00220-013-1738-6.

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44

Wu, Yaping. "Orbital stability of solitary waves of Zakharov system." Journal of Mathematical Physics 35, no. 5 (1994): 2413–22. http://dx.doi.org/10.1063/1.530512.

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45

Hadouaj, Hichem, Boris A. Malomed, and Gérard A. Maugin. "Soliton-soliton collisions in a generalized Zakharov system." Physical Review A 44, no. 6 (1991): 3932–40. http://dx.doi.org/10.1103/physreva.44.3932.

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46

Fang, Yung-Fu, and Kuan-Hsiang Wang. "Local well-posedness for the quantum Zakharov system." Communications in Mathematical Sciences 18, no. 5 (2020): 1383–411. http://dx.doi.org/10.4310/cms.2020.v18.n5.a9.

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47

Wang, Chuan-Jian, Zheng-De Dai, and Gui Mu. "New Homoclinic and Heteroclinic Solutions for Zakharov System." Communications in Theoretical Physics 58, no. 5 (2012): 749–53. http://dx.doi.org/10.1088/0253-6102/58/5/21.

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48

Fang, Yung-Fu, Jun-ichi Segata, and Tsung-Fang Wu. "On the standing waves of quantum Zakharov system." Journal of Mathematical Analysis and Applications 458, no. 2 (2018): 1427–48. http://dx.doi.org/10.1016/j.jmaa.2017.10.033.

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49

Yin, Fu Qi, Sheng Fan Zhou, Zi Gen Ouyang, and Cui Hui Xiao. "Attractor for lattice system of dissipative Zakharov equation." Acta Mathematica Sinica, English Series 25, no. 2 (2009): 321–42. http://dx.doi.org/10.1007/s10114-008-5595-8.

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50

Gauckler, Ludwig. "On a splitting method for the Zakharov system." Numerische Mathematik 139, no. 2 (2018): 349–79. http://dx.doi.org/10.1007/s00211-017-0942-2.

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