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Qualitative analysis and asymptotics of solutions of generalized KdV-class equations

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Abstract

We study the asymptotics and the structure of solutions of generalized KdV-class equations with an arbitrary nonlinearity index, which are extensively used in the physics of ionospheric and magnetospheric plasma, hydrodynamics, and aerodynamics. KdV-class equations are generalized by introducing higher-order dispersion correction and terms describing dissipation and instability caused by numerous factors. Using asymptotic analysis and analysis of solutions in the phase space, we distinguish among different classes of solutions of soliton and nonsoliton types.

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Authors
  1. V. Yu. Belashov
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  2. S. G. Tyunina
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Additional information

North-East Complex Research Institute of the Far East Branch of Russian Academy of Sciences; Pedagogical University, Magadan, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 3, pp. 328–344, March, 1997.

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Belashov, V.Y., Tyunina, S.G. Qualitative analysis and asymptotics of solutions of generalized KdV-class equations. Radiophys Quantum Electron 40, 210–222 (1997). https://doi.org/10.1007/BF02676345

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  • DOI: https://doi.org/10.1007/BF02676345

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