Nonlinear superposition formulae of the Ito equation and a model equation for shallow water waves

1991 ◽  
Vol 24 (9) ◽  
pp. 1979-1985 ◽  
Author(s):  
Xing-Biao Hu ◽  
Yong Li
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Model Equation ◽  
Shallow Water Waves ◽  
Nonlinear Superposition ◽  
Ito Equation

scholarly journals Analytical Treatment of the Generalized Hirota-Satsuma-Ito Equation Arising in Shallow Water Wave

2021 ◽  
Vol 2021 ◽  
pp. 1-26
Author(s):  
Fan Yong-Yan ◽  
Jalil Manafian ◽  
Syed Maqsood Zia ◽  
Dinh Tran Ngoc Huy ◽  
Trung-Hieu Le
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Bilinear Operator ◽  
Shallow Water Waves ◽  
Analytical Treatment ◽  
Kink Wave ◽  
Physical Phenomena ◽  
Hirota Bilinear ◽  
Ito Equation ◽  
Selection Of

In the current study, an analytical treatment is studied starting from the 2 + 1 -dimensional generalized Hirota-Satsuma-Ito (HSI) equation. Based on the equation, we first establish the evolution equation and obtain rational function solutions by means of the bilinear form with the help of the Hirota bilinear operator. Then, by the suggested method, the periodic, cross-kink wave solutions are also obtained. Also, the semi-inverse variational principle (SIVP) will be utilized for the generalized HSI equation. Two major cases were investigated from two different techniques. Moreover, the improved tan χ ξ method on the generalized Hirota-Satsuma-Ito equation is probed. The 3D, density, and contour graphs illustrating some instances of got solutions have been demonstrated from a selection of some suitable parameters. The existing conditions are handled to discuss the available got solutions. The current work is extensively utilized to report plenty of attractive physical phenomena in the areas of shallow water waves and so on.

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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