Abstract We examine the spectral stability and instability of periodic traveling waves for regularized long-wave models. Examples include Boussinesq, Benney–Luke, Benjamin–Bona–Mahony equations. Of particular interest is a striking new phenomenon—spectrum off imaginary axis extending into infinity. The spectrum linearized operator generalized Korteweg–de Vries equation, instance, lies along out...

The equal width (EW) equation for long waves propagating in the positive x-direction, has the form 0    xxt x t u uu u   (6.1.1) where  and  are positive constants, which require the boundary conditions 0  u as   x .The EW equation is a model nonlinear partial differential equation for the simulation of one-dimensional wave propagation in nonlinear media with dispersion process. Soli...

The edge of chaos is analyzed in a spatially extended system, modeled by the regularized long-wave equation, prior to the transition to permanent spatiotemporal chaos. In the presence of coexisting attractors, a chaotic saddle is born at the basin boundary due to a smooth-fractal metamorphosis. As a control parameter is varied, the chaotic transient evolves to well-developed transient turbulenc...