On a variational principle for the fractal Wu–Zhang system arising in shallow water

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Yan-Hong Liang ◽  
Kang-Jia Wang
Keyword(s):  
Variational Principle ◽  
Shallow Water

Perturbation of shallow water waves by semi-inverse variational principle

2013 ◽  
Vol 87 (6) ◽  
pp. 567-569 ◽  
Author(s):  
A. Biswas ◽  
D. M. Milovic ◽  
S. Kumar ◽  
A. Yildirim
Keyword(s):  
Variational Principle ◽  
Shallow Water ◽  
Water Waves ◽  
Shallow Water Waves

scholarly journals Variational principle of the Whitham-Broer-Kaup equation in shallow water wave with fractal derivatives

2021 ◽  
pp. 19-19
Author(s):  
Wei-Wei Ling ◽  
Pin-Xia Wu
Keyword(s):  
Variational Principle ◽  
Shallow Water ◽  
Solitary Waves ◽  
Water Waves ◽  
Water Wave ◽  
Variational Formulation ◽  
Inverse Method ◽  
Solution Structure ◽  
Shallow Water Waves ◽  
Fractal Space

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.

Spatial assemblage structure of shallow-water reef fish in Southwest Australia

2020 ◽  
Vol 649 ◽  
pp. 125-140
Author(s):  
DS Goldsworthy ◽  
BJ Saunders ◽  
JRC Parker ◽  
ES Harvey
Keyword(s):  
Shallow Water ◽  
Reef Fish ◽  
Marine Environment ◽  
Fish Assemblages ◽  
Canopy Cover ◽  
Reef Fishes ◽  
Reef Fish Assemblage ◽  
Reef Type ◽  
Present Distribution ◽  
Southwest Australia

Bioregional categorisation of the Australian marine environment is essential to conserve and manage entire ecosystems, including the biota and associated habitats. It is important that these regions are optimally positioned to effectively plan for the protection of distinct assemblages. Recent climatic variation and changes to the marine environment in Southwest Australia (SWA) have resulted in shifts in species ranges and changes to the composition of marine assemblages. The goal of this study was to determine if the current bioregionalisation of SWA accurately represents the present distribution of shallow-water reef fishes across 2000 km of its subtropical and temperate coastline. Data was collected in 2015 using diver-operated underwater stereo-video surveys from 7 regions between Port Gregory (north of Geraldton) to the east of Esperance. This study indicated that (1) the shallow-water reef fish of SWA formed 4 distinct assemblages along the coast: one Midwestern, one Central and 2 Southern Assemblages; (2) differences between these fish assemblages were primarily driven by sea surface temperature, Ecklonia radiata cover, non-E. radiata (canopy) cover, understorey algae cover, reef type and reef height; and (3) each of the 4 assemblages were characterised by a high number of short-range Australian and Western Australian endemic species. The findings from this study suggest that 4, rather than the existing 3 bioregions would more effectively capture the shallow-water reef fish assemblage patterns, with boundaries having shifted southwards likely associated with ocean warming.

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