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Journal of Mathematical Physics / Volume 52 / Issue 4 / ARTICLES / Methods of Mathematical Physics

J. Math. Phys. 52, 043523 (2011); http://dx.doi.org/10.1063/1.3580272 (16 pages)

Bell-polynomial approach and N-soliton solution for the extended Lotka–Volterra equation in plasmas

Bo Qin1, Bo Tian1,2,3, Li-Cai Liu1, Ming Wang1, Zhi-Qiang Lin1, and Wen-Jun Liu1

1School of Science, P.O. Box 122, Beijing University of Posts and Telecommunications, Beijing 100876, China
2State Key Laboratory of Software Development Environment, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
3Key Laboratory of Information Photonics and Optical Communications (BUPT), Ministry of Education, P.O. Box 128, Beijing University of Posts and Telecommunications, Beijing 100876, China

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(Received 27 November 2010; accepted 24 March 2011; published online 29 April 2011)

Symbolically investigated in this paper is the extended Lotka–Volterra (ELV) equation, which can govern the kinetics of the discrete peaks of the weak Langmuir turbulence in plasmas without the linear damping and random noise. Binary Bell polynomials are applied to the bilinearization of the discrete system. Bilinear Bäcklund transformation of the ELV equation is constructed. N-soliton solution in terms of the extended Casorati determinant is also presented and verified. Propagation and interaction behaviors of the Langmuir turbulence are analyzed. It is demonstrated that the number of the interacting Langmuir waves can influence the soliton velocity and amplitude as well as the collision phase shift. Graphic illustrations of the solitonic collisions show that the repulsion effects and nonlinear interactions are also associated with the number of the interacting Langmuir waves.

© 2011 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. BILINEARIZATION OF THE EXTENDED LOTKA–VOLTERRA EQUATION
  3. BILINEAR BÄCKLUND TRANSFORMATION OF THE EXTENDED LOTKA–VOLTERRA EQUATION
  4. N -SOLITON SOLUTION FOR THE EXTENDED LOTKA–VOLTERRA EQUATION
  5. PROPAGATION AND INTERACTIONS OF THE LANGMUIR TURBULENCE
  6. DISCUSSIONS AND CONCLUSIONS

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KEYWORDS and PACS

Keywords

plasma Langmuir waves, plasma turbulence, polynomials, predator-prey systems, solitons

PACS

  • 52.35.Mw

    Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)

  • 52.35.Ra

    Plasma turbulence

  • 52.35.Fp

    Electrostatic waves and oscillations (e.g., ion-acoustic waves)

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3580272

PUBLICATION DATA

ISSN

0022-2488 (print)  
1089-7658 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
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