Abstract

Splitting Up of Multistable Solitons in Solids

A.I.Potapov, S.V.Gromov, V.V.Kazhaev (Mechanical Engineering Research Institute of Russian Academy of Sciences, Nizhny Novgorod, Russia)

e-mail: apotapov@sandy.ru

The strongly nonlinear particle-like waves described by an equation with cubic nonlinearity and anomalous dispersion are studied. Such waves possess some properties which distinguish them from the classical solitons. The analysis of numerical modelling results shows that, on numerous occasions, the localized waves behave like solitons. They propagate, as solitons do, at a constant velocity that depends on the amplitude and are stable with respect to small perturbations. If the wave amplitudes are above a certain threshold value then they will split up on the head-on collisions giving rise to the secondary particle-like waves and a quasi-linear wave train [V.V. Kazhaev, A. I. Potapov and N. P. Semerikova, Splitting-up of particle-like waves under head-on collision. Radiophysics and Quantum Electronics, 1995, v 38, No 1-2, pp.67-70]. [1, 2] Results of experimental data on propagation and interaction of nonlinear transverse waves in a thin rubber belt are given [A.I. Potapov, A.I. Vesnitsky, Interaction of solitary waves under head on collisions. Experimental investigation. Wave Motion, 1994, v.19, pp. 29-35]. The research described in this paper was made possible by RFBR (grants N 00-02-16582 and N 01-01-00386).

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