Acta Scientific Computer Sciences

Review Article Volume 4 Issue 7

Spectral Approach to Numerical Integration of the GKP or Belashov Class Equations in the Problems of Nonlinear Wave Dynamics Simulation

Vasily Yu Belashov*

Kazan Federal University, Kazan, Russia

*Corresponding Author: Vasily Yu Belashov, Kazan Federal University, Kazan, Russia.

Received: May 12, 2022; Published: June 15, 2022

Abstract

The original method for numerical integration of the generalized Kadomtsev-Petviashvili (KP) equation which includes the term proportional to the fifth derivative (so called the Belashov-Karpman equation) which enables to study the solution's evolution and the multidimensional soliton's interaction's dynamics is presented. This method is rather simple in its computer realization and not such cumbersome comparatively with other known methods for the numerical integration of the different equations of the KP-class. In the paper we consider spectral approach to the numerical integration of the equations of the KP-class describing the dynamics of the ion-acoustic and magnetosonic waves in a plasma on the basis of the generalized KP equation. The method is rather simple in its computer realization and doesn’t such cumbersome comparatively with other methods for the numerical integration of the differential equations of the KP-class, and very effective, so it doesn't require big time and memory expenditures. This approach was first used by us for study of some problems of nonlinear evolution of the fast magnetosonic (FMS) wave beam in magnetized plasma and can be generalized easily for all equations of the KP class.

Keywords: Dynamics; Fast Magnetosonic (FMS); KP-Class

References

  1. VYu Belashov. Proc. ISSS-5, Kyoto, Japan, 118 (1997).
  2. VYu Belashov and SV Vladimirov. “Solitary Waves in Dispersive Complex Media”. Springer-Verlag GmbH and Co.KG (2005).
  3. VI Petviashvili. Sov. Plasma Physics 2 (1976): 469.
  4. VYu Belashov. Plasma Physics and Controlled Fusion 36 (1994): 1661.
  5. YuA Berezin. “Nonlinear wave processes simulation”. Novosibirsk, Nauka (1982).
  6. BB Kadomtsev and VI Petviashvili. Sov. Doklady Physics 192 (1970): 753-756.
  7. VE Zakharov., et al. “Theory of solitons”. Moscow, Nauka (1980).

Citation

Citation: Vasily Yu Belashov. “Spectral Approach to Numerical Integration of the GKP or Belashov Class Equations in the Problems of Nonlinear Wave Dynamics Simulation". Acta Scientific Computer Sciences 4.7 (2022): 41-45.

Copyright

Copyright: © 2022 Vasily Yu Belashov. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.




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