Normal forms application for studying solitary wave solutions of non-integrable evolution systems

摘要

In this paper the problem of obtaining soliton-like solutions to the non-integrable evolution system is discussed. Self-similarity methods together with the normal forms technique are shown to provide significant information on the possibility that such solutions appear. Qualitative investigations, backed by the numerical simulation, are applied to a reactive hydrodynamic model. It is evidenced that this model has a one-parameter family of solitary wave solutions. In addition, the expressions for coefficients of the normal form, corresponding to dynamic systems with (0, +-iΩ) degeneracy of the linear parts, are obtained.