Abstract
Nondissipative and weakly dissipative discontinuity structures are considered. A special numerical method for studying periodic waves is used. The location of branches of periodic solutions is investigated. Solitary waves and nondissipative discontinuity structures are sought as limiting solutions. It is found that, in addition to the resonance of long Alfvén waves with short fast and slow magnetosonic waves, there is also resonance with long waves, which leads to the occurrence of hybrid-type solitary waves and hybrid-type discontinuity structures. Partial differential equations are solved to find out if the found structures are actually observed.
This is a preview of subscription content, log in via an institution to check access.
REFERENCES
A. G. Kulikovskii and G. A. Lyubimov, Magnetic Hydrodynamics (Logos, Moscow, 2005) [in Russian].
S. I. Vainshtein, A. M. Bykov, and I. N. Toptygin, Turbulence, Current Layers, and Shockwaves in Space Plasma (Nauka, Moscow, 1989) [in Russian].
T. Kakutani, H. Ono, T. Taniuti, and C. Wei, “Reductive perturbation method in nonlinear wave propagation. II. Application to hydromagnetic waves in a cold plasma,” J. Phys. Soc. Jpn 24, 1159–1166 (1968).
T. Kakutani and H. Ono, “Weak nonlinear hydromagnetic waves in a cold collision-free plasma,” J. Phys. Soc. Japan 26, 1305–1318 (1969).
A. Il’ichev, “Steady waves in a cold plasma,” J. Plasma Phys. 55, 181–194 (1996).
A. T. Il’ichev, “Solitary wave trains in a cold plasma,” Fluid Dyn. 31, 754–760 (1996).
A. T. Il’ichev, Solitray Waves in Hydromechanics (Fizmatlit, Moscow, 2003) [in Russian].
M. B. Gavrikov, Two-Fluid Hydrodynamics (KRASAND, Moscow, 2018) [in Russian].
I. B. Bakholdin, “Analysis of two-fluid plasma in the electromagnetic hydrodynamics approximation and discontinuous structures in their solutions,” Comput. Math. Math. Phys. 68, 436–452 (2021).
I. B. Bakholdin and A. T. Ilichev, “Fast magnetosonic solitonic structures in a quasi-neutral collision-free finite-beta plasma,” Wave Motion 112, 102936 (2022).
I. B. Bakholdin, “Nondissipative discontinuity structures and solitary waves in solutions to equations of two-fluid plasma in the electromagnetic hydrodynamics approximation,” Comput. Math. Math. Phys. 62, 2139–2153 (2022).
I. B. Bakholdin, Nondissipative Discontinuities in Continuum Mechanics (Fizmatlit, Moscow, 2004) [in Russian].
I. B. Bakholdin, “Time-invariant and time-varying discontinuity structures for models described by the generalized Korteweg-Burgers equation,” J. Appl. Math. Mech. 75 (2), 189–209 (2011).
I. B. Bakholdin, “Theory and classification of the reversible structures of discontinuities in hydrodynamic-type models,” J. Appl. Math. Mech. 78, 599–612 (2014).
I. B. Bakholdin, “Equations describing waves in tubes with elastic walls and numerical methods with low scheme dissipation,” Comput. Math. Math. Phys. 60, 1185–1198 (2020).
E. Lombardi, “Orbits homoclinic to exponentially small periodic orbits for a class of reversible systems,” Arch. Rat. Mech. Anal. 137, 227–304 (1997).
V. I. Arnol’d, Mathematical Methods of Classical Mechanics (Nauka, Moscow, 1989; Springer, New York, 1989).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
The author declares that he has no conflicts of interest.
Additional information
Translated by A. Klimontovich
Publisher’s Note.
Pleiades Publishing remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Bakholdin, I.B. Discontinuity Structures and Solitary Waves in Electromagnetic Hydrodynamics Associated with Linear and Nonlinear Alfvén Wave Resonances. Comput. Math. and Math. Phys. 63, 2123–2138 (2023). https://doi.org/10.1134/S0965542523110039
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0965542523110039