On the theory of solitons in systems with dissipation (Q1821648)

In the weakly nonlinear approximation wave processes in flowing films, the propagation of concentration waves in chemical reactions, the hydrodynamic instability of a laminar flame, and thermocapillary convection in a thin layer are described by equations of the type \(h_ t+4hh_ x+h_{xx}+h_{xxxx}=0\). A special role in wave processes is played by nonlinear localized signals - solitary waves or solitons. In this paper the methods of the theory of dynamical systems are used to carry out a full investigation of solutions of the stationary soliton type for the above-mentioned equation.