Abstract
In this chapter we sketch the basic mathematical equations, adding general relations and inhomogeneity or boundary conditions as a reason for guide formation in a plasma, and illustrating them with simple examples.
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References
V.I. Petviahsvili, Fiz. Plasmy SSSR I, 28 (1975)
V.L. Ginsburg, A.A. Rukhadze, Waves in Magnetoactive Plasma (Nauka, Moscow, 1975)
V.P. Silin, Introduction to the Kinetic Theory of Gases (Lebedev Inst Press, Moscow, 1998), in Russian
A.A. Vlasov, J. Exp. Theor. Phys. 8, 291 (1938)
L.D. Landau, J. Exp. Theor. Phys. 16, 574 (1946)
S.B. Leble, Waveguide Propagation of Nonlinear Waves in Stratified Media (Leningrad University Press, Leningrad, 1988), in Russian; extended edn. (Springer, Berlin, 1990)
D. Bohm, E.P. Gross, Theory of plasma oscillations. Excitation and damping of oscillations. Phys. Rev. 75, 1864 (1949)
V.P. Silin, V.T. Tikhonchuk, J. Exp. Theor. Phys. 81, 2039–2051 (1981)
V.M. Babich, V.S. Buldyrev, I.A. Molotkov, Space-Time Ray Method: Linear and Nonlinear Waves (Leningrad University Press, Leningrad, 1985)
I.V. Karpov, S.B. Leble, V.M. Smertin, Geomagnet. Aeron. SSSR 4, 672–673 (1983)
A.A. Zaitsev, S.B. Leble, Theory of Nonlinear Waves (Kaliningrad University Press, Kaliningrad, 1984)
V.E. Zakharov, S.V. Manakov, S.P. Novikov, J.P. Pitaevski, Theory of Solitons. The Method of Inverse Problems (Nauka, Moscow 1980); [English: Plenum, New York 1984]
V.I. Petviashvili, Vopr. Teor. Piaz. 9(11), 59–82 (1979)
L.M. Gorbunov, V.P. Silin, J. Exp. Theor. Phys. 47, 203–210 (1964)
L.M. Gorbunov, A.M. Tunerbulatov, J. Exp. Theor. Phys. 53, 1494–1497 (1967)
V.P. Maslov: Mathematical Aspects of Integral Optics, Moscow Institute of Electronic Engineering (1983)
SYu. Dobrokhotov, V.P. Maslov, Soviet Science Review, vol. 3 (Overseas Publishing Association, Harwood, 1982), pp. 221–311
V.E. Zakharov, J. Exp. Theor. Phys. 62, 1745–1755 (1972)
V.I. Talanov, ZhETF Pis. Red. 2, 223 (1965) [JETP Lett. 2, 141 (1965)]; V.E. Zakharov: J. Appl. Mech. Tech. Phys. 9, 190 (1968)
V.E. Zakharov, A.B. Shabat: (1971) Exact theory of two-dimensional self- focusing and one-dimensional modulation of waves in nonlinear media. Zhurn. Eksp. Teor. Fiz. 61, 118–134 [(1972). Sov. Phys. JETP 34, 62–69]
S.B. Leble, D.W. Rohraff, Nonlinear evolution of components of an electromagnetic field of helicoidal waves in plasma. Phys. Scr. 123, 140–144 (2006)
V.P. Dmitriyev, Helical waves on a vortex filament. Am. J. Phys. 73, 563 (2005). https://doi.org/10.1119/1.1873892
G. Sato, W. Oohara, R. Hatakeyama, Plasma production by helicon waves with single mode number in low magnetic fields, in 12th International Congress on Plasma Physics, 25–29 October 2004, Nice (France)
E. Doktorov, S.B. Leble, Dressing Method in Mathematical Physics (Springer, Berlin, 2007)
B.G. Konopelchenko, Introduction to Multidimensional Integrable Equations: The Inverse Spectral inverse spectral transform in 2+1 dimensions (Plenum Press, New York, 1992)
S. Shinohara, K. Shamrai, Direct comparison of experimental and theoretical results on the antenna loading and density jumps in a high pressure helicon source. Plasma Phys. Control. Fusion 42, 865–880 (2000)
B.W. Maxfield, Helicon waves in solids. Am. J. Phys. 37(3), 241–269 (1969)
S. Leble, M. Salle, The Darboux transformations for the discrete analogue of the Silin-Tikhonchuk equation. Dokl. AN SSSR 284, 110–114 (1985)
T.J. Cui, D.R. Smith, R. Liu (eds): Metamaterials: Theory, Design, and Applications (Springer, Berlin, 2010)
R.W. Ziolkowski, A. Kipple, Causality and double-negative metamaterials. Phys. Rev. E 68, 026615 (2003)
R.W. Ziolkowski, F. Auzanneau, Passive artificial molecule realizations of dielectric materials. J. Appl. Phys. 82, 3195–3198 (1997)
K.V. Pravdin, I.Y. Popov, Layered system with metamaterials. J. Phys.: Conf. Ser. 661(1), 012025 (2015)
A.A. Perelomova, Projectors in nonlinear evolution problem: acoustic solitons of bubbly liquid. Appl. Math. Lett. 13, 93–98 (2000); Nonlinear dynamics of vertically propagating acoustic waves in a stratified atmosphere. Acta Acustica 84 (6), 1002–1006 (1998)
S.V. Sazonov, N.V. Ustinov, New class of extremely short electromagnetic solitons. General class of the traveling waves propagating in a near oppositely-directional coupler. Pis’ma v Zh. Eksper. Teoret. Fiz. 83(11), 573–578 (2006)
T. Schäfer, C.E. Wayne, Propagation of ultra-short optical pulses in cubic nonlinear media. Phys. D 196, 90–105 (2004)
Y. Chung, C.K.R.T. Jones, T. Schäfer, C.E. Wayne, Ultra-short pulses in linear and nonlinear media. Nonlinearity 18, 1351–1374 (2004)
Z. Zhaqilao, Q. Hu, Z. Qiao, Multi-soliton solutions and the Cauchy problem for a two-component short pulse system. Nonlinearity 30(10), 3773 (2017)
P. Kinsler, Phys. Rev. A 81, 023808 (2010)
V.V. Belov, SYu. Dobrokhotov, T.Y.A. Tudorovskiy, Operator separation of variables for adiabatic problem in quantum and wave mechanics. J. Eng. Math. 55(1–4), 183–237 (2006)
M. Kuszner, S. Leble, Directed electromagnetic pulse dynamics: projecting operators method. J. Phys. Soc. Jpn. 80, 024002 (2011)
A. Perelomova, Development of linear projecting in studies of non-linear flow. Acoustic heating induced by non-periodic sound. Phys. Lett. A 357, 42–47 (2006)
M. Kuszner, S. Leble, Ultrashort opposite directed pulses dynamics with Kerr effect and polarization account. J. Phys. Soc. Jpn. 83, 034005 (2014)
K. Porsezian, V.C. Kuriakose, Optical Solitons (Springer, Berlin, 2003)
S. Pitois, G. Millot, S. Wabnitz, Nonlinear polarization dynamics of counterpropagating waves in an isotropic optical fiber: theory and experiments. J. Opt. Soc. Am. B 18(4) (2001)
S. Leble, D. Ampilogov, Directed electromagnetic wave propagation in 1D metamaterial: projecting operators method phys. Lett. A 380(29–30), 2271–2278 (2016)
D. Ampilogov, S. Leble, General equation for directed electromagnetic wave propagation in 1D metamaterial: projecting operator method. TASK Q. 20(2) (2016)
D. Ampilogov, S. Leble, Interaction of orthogonal-polarized waves in 1D metamaterial with Kerr nonlinearity, arXiv:1802.09523 [physics.optics]; D. Ampilogov: Interaction of orthogonal-polarized waves in 1D-metamaterial. TASK Q. 21(2), 605–619 (2017)
S. Leble, A. Perelomova, Dynamical Projectors Method in Hydro- and Electrodynamics (CRC Press, Taylor and Francis, Boca Raton, 2018)
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Leble, S. (2019). Guide Propagation and Interaction of Plasma Waves. Metamaterials. In: Waveguide Propagation of Nonlinear Waves. Springer Series on Atomic, Optical, and Plasma Physics, vol 109. Springer, Cham. https://doi.org/10.1007/978-3-030-22652-7_7
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