## Abstract

The choice of the expansion parameter employed in the analysis of the equations of weakly relativistic plasma affects the physical significance of the results.

Traditionally, the small parameter employed in the non-relativistic and weak relativistic limits has been the order of magnitude of (v/v0), where v is the ion velocity, and v0 is proportional to the average electron velocity. However, in the weak relativistic case, the order of magnitude of (v/c), where c is the speed of light is the more natural choice. The resulting KdV equation with perturbations through second order is analyzed through a Normal Form expansion. The analysis exposes physical effects in corrections beyond lowest order, which hitherto have not be

identified: (1) Effect of localized soliton interaction region; (2) Long-range interactions among solitons; (3) Dispersive waves generated by soliton interactions.

In addition, the analysis provides information regarding: (1) Clear distinction between non-relativistic and weak relativistic effects; (2) Clear separation between relativistic and electron-temperature effects; (3) Variation of the effective small parameter used in the series expansion of the solution as the average electron kinetic energy is increased. These qualitative features do not depend on the details of the electron-gas thermodynamic distribution

Traditionally, the small parameter employed in the non-relativistic and weak relativistic limits has been the order of magnitude of (v/v0), where v is the ion velocity, and v0 is proportional to the average electron velocity. However, in the weak relativistic case, the order of magnitude of (v/c), where c is the speed of light is the more natural choice. The resulting KdV equation with perturbations through second order is analyzed through a Normal Form expansion. The analysis exposes physical effects in corrections beyond lowest order, which hitherto have not be

identified: (1) Effect of localized soliton interaction region; (2) Long-range interactions among solitons; (3) Dispersive waves generated by soliton interactions.

In addition, the analysis provides information regarding: (1) Clear distinction between non-relativistic and weak relativistic effects; (2) Clear separation between relativistic and electron-temperature effects; (3) Variation of the effective small parameter used in the series expansion of the solution as the average electron kinetic energy is increased. These qualitative features do not depend on the details of the electron-gas thermodynamic distribution

Original language | English |
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Pages (from-to) | 32-47 |

Number of pages | 16 |

Journal | Journal of Applied Mathematics and Computation |

Volume | 5 |

Issue number | 1 |

State | Published - 2021 |