Time-fractional generalized Boussinesq equation for Rossby solitary waves with dissipation effect in stratified fluid and conservation laws as well as exact solutions

2018 ◽  
Vol 327 ◽  
pp. 104-116 ◽  
Author(s):  
Changna Lu ◽  
Chen Fu ◽  
Hongwei Yang
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Solitary Waves ◽  
Boussinesq Equation ◽  
Stratified Fluid ◽  
Dissipation Effect ◽  
Rossby Solitary Waves ◽  
Generalized Boussinesq Equation

scholarly journals Exact Solutions and Conservation Laws of the (3 + 1)-Dimensional B-Type Kadomstev–Petviashvili (BKP)-Boussinesq Equation

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 97 ◽  
Author(s):  
Ben Gao ◽  
Yao Zhang
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Boussinesq Equation ◽  
Lie Symmetry ◽  
Optimal System ◽  
Lie Symmetry Analysis ◽  
One Dimensional ◽  
Reduced Equations ◽  
Tanh Method ◽  
Similarity Reductions

In this paper, Lie symmetry analysis is presented for the (3 + 1)-dimensional BKP-Boussinesq equation, which seriously affects the dispersion relation and the phase shift. To start with, we derive the Lie point symmetry and construct the optimal system of one-dimensional subalgebras. Moreover, according to the optimal system, similarity reductions are investigated and we obtain exact solutions of reduced equations by means of the Tanh method. In the end, we establish conservation laws using Ibragimov’s approach.

scholarly journals Nonlinear self adjointness, conservation laws and exact solutions of ill-posed Boussinesq equation

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 37-43 ◽  
Author(s):  
Emrullah Yaşar ◽  
Sait San ◽  
Yeşim Sağlam Özkan
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Shallow Water ◽  
Water Waves ◽  
Function Method ◽  
Boussinesq Equation ◽  
Lie Point Symmetries ◽  
Shallow Water Waves ◽  
Non Linear ◽  
Ill Posed

AbstractIn this work, we consider the ill-posed Boussinesq equation which arises in shallow water waves and non-linear lattices. We prove that the ill-posed Boussinesq equation is nonlinearly self-adjoint. Using this property and Lie point symmetries, we construct conservation laws for the underlying equation. In addition, the generalized solitonary, periodic and compact-like solutions are constructed by the exp-function method.

scholarly journals Conservation laws and exact solutions for the generalized Ostrovsky equation using symmetry analysis

2021 ◽  
Author(s):  
Sol Sáez
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Conservation Laws ◽  
Exact Solutions ◽  
Solitary Waves ◽  
Symmetry Analysis ◽  
Partial Differential ◽  
Wide Range ◽  
Depth Study ◽  
Ostrovsky Equation

In this work we consider a generalized Ostrovsky equation depending on two arbitrary functions and we make an in-depth study of this equation. We obtain the Lie symmetries which are admitted by this equation and some exact solutions as a periodic or solitary waves, obtained through ordinary and partial differential equations. Also, by means of the concept of multiplier, we obtain a wide range of conservation laws which preserve properties of the generalized Ostrovsky equation.

scholarly journals Conservation laws for a Boussinesq equation.

2017 ◽  
Vol 2 (2) ◽  
pp. 465-472 ◽  
Author(s):  
M.L. Gandarias ◽  
M.S. Bruzón
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Conservation Laws ◽  
Boussinesq Equation ◽  
Point Of View ◽  
Multiplier Method ◽  
Third Order ◽  
Order Ordinary Differential Equation ◽  
Generalized Boussinesq Equation ◽  
The Relationship

AbstractIn this work, we study a generalized Boussinesq equation from the point of view of the Lie theory. We determine all the low-order conservation laws by using the multiplier method. Taking into account the relationship between symmetries and conservation laws and applying the multiplier method to a reduced ordinary differential equation, we obtain directly a second order ordinary differential equation and two third order ordinary differential equations.

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