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The solitons as macroscopic analogues of the quantum particles arise in different systems.
In the present work we research "heat" solitons, not being only by physical processes.
On the basis of the solutions of the Maxwell's nonlinear equations and nonlinear heat transfer equation the solutions in form solitons for the temperature T are received. We assumed that a heat source depends on temperature as polynom. In particular, such solutions show on the stabilization of the process: the increase of an external heat source in the certain limits does not increase temperature. The arbitrary dependences q(T) and possible phase transitions on border of two mediums are considered, and corresponding soliton solutions are received. The received results with non-stationary non-linear transport equations allow to investigate the heat solitons arisen at influence ultra-short pulses generated by laser systems (for example, nanosystems [1],
biosystems). For quadratic dependence q(T) we used in particular the method suggested in [2]. The received results (for the description of the transport processes and external influences) and the known fact of repeatability of psychological situations allow consider the modification of the information (revealed isolated situation to following similar) as the soliton process. The corresponding calculation of the fractal dimension does not take account a change into time and mechanisms of transition, though allows receive the approached results. The solutions in form dissipative solitons allow of the corresponding non-linear equations allow fill this gap. This work was supported by the Russian Fund for Basic Research (Grant No. 03-01-00324). References 1. L.A. Uvarova, T.V. Kazarova. Modelling of transport processes in nanosystems in conditions of external influences//Workshop on "Generation and Health Effects of Nanoparticles", Karlsruhe, Germany, 2005. 2. W. Sarlet. First integrals for one dimensional particle motion in a non-linear time-dependent potential field// Int. J. Non-linear Mech., V. 18, N 4. P. 259-268 (1983). |
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