Extended KdV equation for the case of uneven bottom

Abstract

We derived consistently, according to the second order perturbation approach, the extended KdV equation for an uneven bottom for the case of $\alpha =O(\beta )$ and $\delta =O({\beta }^2)$. This equation can be obtained only when the bottom is given by a piecewise linear function. For the case of $\alpha =O(\beta )$ and $\delta =O(\beta )$, a unidirectional wave equation is derived in the first order approach with the same limitation for the bottom profile.

6 pages, 5 figures, derivations of final wave equations corrected

References in corpus (3)

• Exact solitonic and periodic solutions of the extended KdV equation
• Single soliton solution to the extended KdV equation over uneven depth
• New exact superposition solutions to KdV2 equation

Cited by in corpus (1)

• What kinds of KdV-type equations are allowed by an uneven bottom