A geometric construction of traveling waves in a generalized nonlinear dispersive–dissipative equation

This paper is concerned with a generalized nonlinear dispersive–dissipative equation which is found in many areas of application including waves in a thermoconvective liquid layer, plasma waves and nonlinear electromagnetic waves. It is known that solitary waves for a special case of this equation are formed ahead of conventional chaotic-like irregular structures. Using a dynamical systems approach, specifically based on geometric singular perturbation theory and center manifold theory, we construct traveling waves for this model equation. This also includes some numerical calculations. The occurrence of solitary waves and oscillatory kink or shock waves is shown.