The effects of generalized dispersion on dissipative dynamical systems (Q1808588)

The authors are interested in an evolution equation arising in the nonlinear stability of the interface separating two immiscible fluids flowing in circular pipe, the so-called core-annular flow, which can be written as \[ u_t+ uu_x+u_{xx}+ \nu u_{xxxx}+ \tfrac{\beta}{\nu} Lu=0, \qquad u\bigl|_{t=0}= u_0(x), \quad u(x+2\pi,t)= u(x,t), \tag{1} \] where \(L\) is the linear dispersion operator. The authors ask and answer to the following question: what is the effect of using a local approximation of \(L\) in (1) as opposed to computing with the full dispersion. They provide the paper by numerical examples.