A geometric construction of traveling waves in a generalized nonlinear dispersive-dissipative equation (Q387271)

The authors construct traveling wave solutions for the following generalized nonlinear dispersive--dissipative equation NEWLINE\[NEWLINE \frac{\partial u}{\partial t} + \alpha u^n \frac{\partial u}{\partial x} + \gamma \frac{\partial^3 u}{\partial x^3} + \epsilon \left( b \frac{\partial^2 u}{\partial x^2} + r \frac{\partial}{\partial x}\Biggl(u \frac{\partial u}{\partial x} \Biggl) + s \frac{\partial^4 u}{\partial x^4}\right), NEWLINE\]NEWLINE describing wave propagation. The dynamical system approach, based on geometric singular pertrubation theory and center manifold theory, is used for investigation. The properties of solution are studied with the help of numerical methods.