Analysis and computation of a nonlinear Korteweg-de Vries system.

The authors consider the Korteweg-de Vries equation with a dissipative term ut+uux+uxxx+a(x)u=0, satisfying a(x)≥a0>0, on finite intervals I. Main results include existence and regularity of solutions with suitable homogeneous boundary conditions and improved decay estimates of ∥u(t)∥L2(I) (i.e. with the rate exp(−(a0+γ)t) for some γ>0), using an idea in [N. A. Larkin, J. Math. Anal. Appl. 297, No. 1, 169–185 (2004; Zbl 1075.35070)]. Moreover, a rigorous numerical of that model is performed.