In this paper, we apply and compare modified Variational Iteration Methods (VIMAP) to find travelling wave solutions of Whitham-Broer-Kaup (WBK) equations. The proposed modifications are made by introducing Adomian’s and He’s polynomials in the correction functional of the VIM. The use of Lagrange multiplier coupled with He’s polynomials explicitly reveal a clear edge over the coupling with Ado...

On the basis of the integrable Kaup–Boussinesq version of the shallow-water equations, an analytical theory of undular bores is constructed. A complete classification for the problem of the decay of an initial discontinuity is made.

Complex systems (CS) are pervasive in many areas, namely financial markets; highway transportation; telecommunication networks; world and country economies; social networks; immunological systems; living organisms; computational systems; and electrical and mechanical structures. CS are often composed of a large number of interconnected and interacting entities exhibiting much richer global scal...