On the use of modified Boussinesq equation for studying double-layered hillslope recession characteristics

2021 ◽  
Vol 603 ◽  
pp. 127041
Author(s):  
Yunan Ding ◽  
Jun Kong ◽  
Jinming Zhang ◽  
Zhaoyang Luo ◽  
Chengji Shen ◽  
...  
Keyword(s):  
Boussinesq Equation ◽  
Modified Boussinesq Equation

scholarly journals An application of the MEFM to the modified Boussinesq equation

2018 ◽  
Vol 9 (1) ◽  
pp. 11-17
Author(s):  
Tolga Akturk
Keyword(s):  
Function Method ◽  
Boussinesq Equation ◽  
Travelling Wave ◽  
3D Graphics ◽  
Travelling Wave Solutions ◽  
Trigonometric Functions ◽  
Wolfram Mathematica ◽  
Modified Boussinesq Equation ◽  
Mathematica Software ◽  
2D And 3D

In this paper, some travelling wave solutions of the Modified Boussinesq (MBQ) equation are obtained by using the modified expansion function method (MEFM). When the obtained solutions are commented, trigonometric functions including hyperbolic features are obtained. The 2D and 3D graphics of the solutions have been investigated by selecting appropriate parameters. All the obtained solutions provide the MBQ equation. In this work, all mathematical calculations are done with Wolfram Mathematica software. 

scholarly journals CRE Solvability, Exact Soliton-Cnoidal Wave Interaction Solutions, and Nonlocal Symmetry for the Modified Boussinesq Equation

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Wenguang Cheng ◽  
Biao Li
Keyword(s):  
Boussinesq Equation ◽  
Wave Interaction ◽  
Original System ◽  
Cnoidal Wave ◽  
Nonlocal Symmetry ◽  
Residual Symmetry ◽  
Symmetry Approach ◽  
Modified Boussinesq Equation ◽  
The Relationship ◽  
Truncated Painlevé Expansion

It is proved that the modified Boussinesq equation is consistent Riccati expansion (CRE) solvable; two types of special soliton-cnoidal wave interaction solution of the equation are explicitly given, which is difficult to be found by other traditional methods. Moreover, the nonlocal symmetry related to the consistent tanh expansion (CTE) and the residual symmetry from the truncated Painlevé expansion, as well as the relationship between them, are obtained. The residual symmetry is localized after embedding the original system in an enlarged one. The symmetry group transformation of the enlarged system is derived by applying the Lie point symmetry approach.

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