Solitons in Disordered Systems or Application of Catastrophe Theory to Solitons
The problem of the soliton existence in a disordered system is connected with the question of the soliton existence in a homogeneous medium . Generally speaking the answer to the question of the existence and stability of solition can be found by means of the mathematical theory of the singularity function, which is usually called as the catastrophe theory . From the point of view of this theory we construct some functional in the functional space of the wave function. From this functional we can obtain the equation, which defines the soliton solution. On the other hand our functional defines some surface S. The extrema of this surface correspond to soliton solution. If we take the minima of this surface then the soliton, corresponding to this stationary point, is a stable one. The other extrema S (different of minima) correspond to an unstable soliton. Let us consider simple examples.
KeywordsSoliton Solution Langmuir Wave Catastrophe Theory Virial Theorem Landau Institute
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