О.V. Druzhinina - Dr. Sc. (Phys.-Math.), Professor, Main Research Scientist, Institute of Informatics Problems of RAS (Moscow). E-mail: ovdruzh@mail.ru Z.L. Shulimanova - Dr. Sc. (Phys.-Math.), Head of Department, Moscow State University of Railway Engineering. E-mail: zinaida110@yandex.ru V.L. Vorontsova - Ph. D. (Phys.-Math.), Associate Professor, Institute of Management, Economics and Finance (Kazan?) T.F. Klimova - Ph. D. (Eng.), Associate Professor, Moscow State University of Railway Engineering

Questions of stability of soliton models are considered. A comparative analysis of solitons stability concepts is presented and the modifications of the stability and instability basic theorems are given in accordance with two measures: Lyapunov-Movchan theorem on stability and Chetaev-Movchan theorem on instability. For stability analysis method of A.A. Shestakov of mathematical modeling of distributed systems by the aid of abstract evolutional equations is used. The global asymptotic stability of soliton solutions is investigated on the basis of Lyapunov functionals properties. Obtained results can be used in stability problems of nonlinear dynamical models.

 

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