Approximate symmetry and exact solutions of the singularly perturbed Boussinesq equation

2017 ◽  
Vol 53 ◽  
pp. 1-9
Author(s):  
Mohammad Rahimian ◽  
Megerdich Toomanian ◽  
Mehdi Nadjafikhah
Keyword(s):  
Exact Solutions ◽  
Boussinesq Equation ◽  
Singularly Perturbed ◽  
Approximate Symmetry

Exact Solutions of Boussinesq Equation

2012 ◽  
Author(s):  
M. A. Jafarizadeh ◽  
A. R. Esfandyari
Keyword(s):  
Exact Solutions ◽  
Boussinesq Equation

Families of exact solutions of a new extended $$\varvec{(2+1)}$$(2+1)-dimensional Boussinesq equation

2018 ◽  
Vol 91 (4) ◽  
pp. 2593-2605 ◽  
Author(s):  
Yulei Cao ◽  
Jingsong He ◽  
Dumitru Mihalache
Keyword(s):  
Exact Solutions ◽  
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.

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