Bona, Jerry L.; Luo, Laihan Decay of solutions to nonlinear, dispersive wave equations. (English) Zbl 0780.35098 Differ. Integral Equ. 6, No. 5, 961-980 (1993). Summary: The asymptotic behavior of solutions to the initial-value problem for the generalized Korteweg-de Vries-Burgers equation \[ u_ t+u_ x+u^ p u_ x- \nu u_{xx}+u_{xxx}=0 \] and the generalized regularized long- wave-Burgers equation \[ u_ t+u_ x+u^ p u_ x- \nu u_{xx}- u_{xxt}=0 \] is studied for \(\nu>0\) and \(p\geq 2\). The decay rate of solutions of these equations is that exhibited by solutions of the linearized equation in which the nonlinear term is simply dropped. Cited in 1 ReviewCited in 19 Documents MSC: 35Q53 KdV equations (Korteweg-de Vries equations) 35B40 Asymptotic behavior of solutions to PDEs 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction 35C15 Integral representations of solutions to PDEs Keywords:asymptotic behavior; initial-value problem; generalized Korteweg-de Vries-Burgers equation; generalized regularized long-wave-Burgers equation; decay rate PDFBibTeX XMLCite \textit{J. L. Bona} and \textit{L. Luo}, Differ. Integral Equ. 6, No. 5, 961--980 (1993; Zbl 0780.35098)