TY - JOUR
TI - Variational theory for a kind of non-linear model for water waves
AU - Ling Wei-Wei
AU - Wu Pin-Xia
JN - Thermal Science
PY - 2021
VL - 25
IS - 2
SP - 1249
EP - 1254
PT - Article
AB - The Whitham-Broer-Kaup equation exists widely in shallow water waves, but unsmooth boundary seriously affects the properties of solitary waves and has certain deviations in scientific research. The aim of this paper is to introduce its modification with fractal derivatives in a fractal space and to establish a fractal variational formulation by the semi-inverse method. The obtained fractal variational principle shows conservation laws in an energy form in the fractal space and also hints its possible solution structure.