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Qualitative Analysis and Asymptotics of Solutions of the Gkp-Class Equations with Variable Dispersion


Affiliations
1 Kazan (Volga Region), Federal University, Kazan, Russian Federation
2 Kazan National Research Technical University Named after A.N. Tupolev, Kazan, Russian Federation
 

In this paper we study the dynamical systems associated with the generalized Kadomtsev-Petviashvili (GKP) equation with variable dispersion and consider the structure of possible multidi-mensional solutions and their asymptotics. We also present some considerations on constructing of the phase portraits of the systems in the 8-dimensional phase space for the GKP equation on the basis of the results of qualitative analysis of the generalized equations of the KdV-class.

Keywords

Dynamical System, Generalized KDV Equation, GKP Equation, Multidimensional Solutions, Phase Space, Qualitative Analysis, Solitons, Structure of Solutions, Variable Dispersion.
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  • Karpman VI, Belashov VYU. Dynamics of two-dimensional solitons in weakly dispersive media. Phys Lett. 1991;154:131-9.

  • Belashov YUV. The KP equation and its generalizations. Theory and applications" Magadan. NEISRI FEB RAS, 1997;162.

  • Belashov VYU, Vladimirov SV. Solitary waves in dispersive complex media. Springer. Verlag GmbH & Co.KG. 2014;305.

  • Kadomtsev BB, Petviashvili VI. Instabilities and oscillations of one- and two-dimensional Kadomtsev-Petviashvili waves and solitons II. Linear to nonlinear analysis. Soviet Phys Dokl.1970; 192:753-756.

  • Belashov VYU, Tunina SG. Astronomy, observations and techniques. Radiophysics and quantum electronics. Soviet Radiophys. XL.1997; 1: 328-44.

  • Belashov VYU. Introduction to plasma physics and controlled fusion. Plasma Phys and Controlled Fusion. 1994;36:1661-69.

  • Belashov VYU., Belashova ES. Geomagnetism and Aeronomy, 2016;56:716-23.

  • Kawahara TJ. A general theory of magnetic resonance absorption. J Phys Soc. Jap. 1972;33:260-64.

  • Belashov VYU. Rectification properties of carbon nanotube “Y-junctions. Phys. Lett. 1995;197:282-86.

  • Kawahara T. Fractional quantization of the hall effect. Phys. Rev. Lett. 1983;51:381-83.

  • Belashov VYU. Numerical analysis of Coriolis effect on low-head hydraulic turbines. J. Astrophys. Aerospace Technol. 2016;4:18.

  • Belashov VYU. Belashova ES. Solar neutron events as a tool to study particle acceleration at the Sun. J Atm. and Solar-Terr. Physics. 2015;136: 150-54.

  • Belashov VYU, Belashova ES. Discover the life sciences in space research. Adv. Space Res. 2015;56:333–40.


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  • Qualitative Analysis and Asymptotics of Solutions of the Gkp-Class Equations with Variable Dispersion

Abstract Views: 230  |  PDF Views: 2

Authors

V. Y. U. Belashov
Kazan (Volga Region), Federal University, Kazan, Russian Federation
S. E. Belashova
Kazan National Research Technical University Named after A.N. Tupolev, Kazan, Russian Federation

Abstract


In this paper we study the dynamical systems associated with the generalized Kadomtsev-Petviashvili (GKP) equation with variable dispersion and consider the structure of possible multidi-mensional solutions and their asymptotics. We also present some considerations on constructing of the phase portraits of the systems in the 8-dimensional phase space for the GKP equation on the basis of the results of qualitative analysis of the generalized equations of the KdV-class.

Keywords


Dynamical System, Generalized KDV Equation, GKP Equation, Multidimensional Solutions, Phase Space, Qualitative Analysis, Solitons, Structure of Solutions, Variable Dispersion.

References