Nonlinear Phenomena in Complex Systems, 2014, Vol.17, No.2, pp.106-115

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2014, Vol.17, No.2, pp.106-115

Nonlinear Effects in Generation of Radiation by Relativistic Electron Beams in One-Dimensional Periodic Structures
G. A. Omel’yanov and M. A. Valdez-Grijalva

We consider KdV-type equations with nonlinearities u^k, k (1, 5), and small dispersion ε. The first result consists in the conclusion that, in the leading term with respect to ε, the solitary waves in this model interact like KdV solitons. Next it turned out that there exists a very interesting scenario of instability in which the short-wave soliton remains stable whereas a small long-wave part, generated by perturbations of original equation, turns to be unstable, growing and destroying the leading term. At the same time, such perturbation can eliminate the collision of solitons. Numerical simulations confirming the results are also presented.

Key words: KdV-type equation, soliton, interaction, ion-acoustic waves, weak asymptotics method, finite differences scheme

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