It is shown that explicit Bäcklund transformations (BTs) for the high-order constrained flows of soliton hierarchy can be constructed via their Darboux transformations and Lax representation, and these BTs are canonical transformations including Bäcklund parameter η and possess a spectrality property with respect to η and the ’conjugated’ variable μ for which the pair (η, μ) lies on the spectra...

To study a nonlinear partial differential equation (PDE), the Painlev́e expansion developed by Weiss, Tabor and Carnevale (WTC) is one of the most powerful methods. In this paper, using any singular manifold, the expansion series in the usual Painlev́e analysis is shown to be resummable in some different ways. A simple nonstandard truncated expansion with a quite universal reduction function is u...

In this paper, we study the possible second order Lax operators for all the possible (1+1)-dimensional models with Schwarz variants and some special types of high dimensional models. It is shown that for every (1+1)-dimensional model and some special types of high dimensional models which possess Schwarz variants may have a second order Lax pair. The explicit Lax pairs for (1+1)-dimensional Kor...

We present a synthesis of the state of knowledge concerning the species of Passalidae (Coleoptera) of the West Indies and we present a key to the species. The recently described genus Antillanax Boucher renders the subgenus Passalus (Pertinax) Kaup paraphyletic, therefore we place Antillanax in synonymy with Passalus (Pertinax) and we propose a new combination for Passalus (Pertinax) doesburgi ...

A new solution to the coupled gravitational and scalar field equations for a condensed boson field is found in Newtonian approximation. The solution is axially symmetric, but not spherically symmetric. For N particles the mass of the object is given by M = Nm − 0.02298NG N m, to be compared with M = Nm− 0.05426NG N m for the spherically symmetric case. Recent developments in particle physics an...

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 scientific research. aim this paper is to introduce its modification with fractal derivatives a space establish variational formulation by semi-inverse method. obtained principle shows conservation laws an energy form also hint...