A rigorous derivation of the extended KdV
equation
Abstract
The interesting background and historical development of KdV equations
were discussed widely. These equations describe the propagation of water waves in
weakly non linear and weakly dispersive medium. Referring to physical derivation of
KdV equations, scientists used to impose shallow water equations, thus the formal or
physical derivation of KdV equations. However, these equations have rarely been derived
rigorously. The aim of this paper is to giving insight into their rigorous mathematical
derivation, instead of only referring to. Thereby, a rigorous derivation of two
extended KdV equations: one on the velocity, other on the surface elevation. With this
aim in mind, the primary research method for this paper will depend on the definition
of consistency. Hence, a rigorous justification of new extended KdV equations will be
provided thanks to this definition. This result provides a precise mathematical answer
to a question raised by several authors in the last years, that is the verification of the
extended KdV equations, derived previously, using formal methods.
Journal/Conference Information
International Conference on Mathematical Models & Computational Techniques in Science & Engineering,Conference Type: International, Organized By: IOP, Proceeding Format: Electronic editions, Conference Date: 02/01/2020,