scholarly journals Non-uniform continuity of the flow map for an evolution equation modeling shallow water waves of moderate amplitude

2014 ◽  
Vol 17 ◽  
pp. 322-331 ◽  
Author(s):  
Nilay Duruk Mutlubaş ◽  
Anna Geyer ◽  
Bogdan-Vasile Matioc
Keyword(s):  
Evolution Equation ◽  
Shallow Water ◽  
Water Waves ◽  
Uniform Continuity ◽  
Equation Modeling ◽  
Shallow Water Waves ◽  
Flow Map

scholarly journals Degeneration of Solitons for a the (3+1)-dimensional Generalized Nonlinear Evolution Equation for the Shallow Water Waves

2021 ◽  
Author(s):  
longxing li ◽  
Long-Xing Li
Keyword(s):  
Evolution Equation ◽  
Shallow Water ◽  
Water Waves ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Rogue Waves ◽  
Shallow Water Waves ◽  
Hirota Bilinear Form ◽  
Wave Limit

Abstract A the (3+1)-dimensional generalized nonlinear evolution equation for the shallow water waves is investigated with different methods. Based on symbolic computation and Hirota bilinear form, Nsoliton solutions are constructed. In the process of degeneration of N-soliton solutions, T-breathers are derived by taking complexication method. Then rogue waves will emerge during the degeneration of breathers by taking the parameter limit method. Through full degeneration of N-soliton, M-lump solutions are derived based on long wave limit approach. In addition, we also find out that the partial degeneration of N-soliton process can generate the hybrid solutions composed of soliton, breather and lump.

RESPONSE CHARACTERISTICS OF GRAVEL BEACH FROM THE VIEWPOINT OF SHALLOW WATER WAVES AND MOVEMENT OF GRAVELS

2020 ◽  
Vol 76 (2) ◽  
pp. I_565-I_570
Author(s):  
Shin-ichi AOKI ◽  
Tomoki HAMANO ◽  
Taishi NAKAYAMA ◽  
Eiichi OKETANI ◽  
Takahiro HIRAMATSU ◽  
...  
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Shallow Water Waves ◽  
Response Characteristics ◽  
Gravel Beach
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