New similarity reductions and exact solutions for helically symmetric viscous flows

2020 ◽  
Vol 32 (5) ◽  
pp. 053604
Author(s):  
Dominik Dierkes ◽  
Alexei Cheviakov ◽  
Martin Oberlack
Keyword(s):  
Exact Solutions ◽  
Viscous Flows ◽  
Similarity Reductions

Similarity reductions and exact solutions for two-dimensional Euler–Boussinesq equations

2019 ◽  
Vol 33 (27) ◽  
pp. 1950328
Author(s):  
En Gui Fan ◽  
Man Wai Yuen
Keyword(s):  
Exact Solutions ◽  
Stream Function ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Boussinesq Equations ◽  
Two Dimensional ◽  
Similarity Reduction ◽  
Wave Solutions ◽  
Similarity Reductions

In this paper, by introducing a stream function and new coordinates, we transform classical Euler–Boussinesq equations into a vorticity form. We further construct traveling wave solutions and similarity reduction for the vorticity form of Euler–Boussinesq equations. In fact, our similarity reduction provides a kind of linearization transformation of Euler–Boussinesq equations.

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.

Similarities and exact solutions of transonic gas flow model

2020 ◽  
Vol 34 (32) ◽  
pp. 2050363
Author(s):  
Zehra Pinar
Keyword(s):  
Steady State ◽  
Exact Solutions ◽  
Nonlinear Wave ◽  
Gas Flow ◽  
Flow Model ◽  
Wave Theory ◽  
Analysis Method ◽  
Classical Symmetry ◽  
Nonlinear Acoustic ◽  
Similarity Reductions

In this work, one of the important models in nonlinear wave theory and also in nonlinear acoustic, the Lin–Reissner–Tsien (LRT) equation is considered. For the homogeneous form of LRT equation, the exact solutions are obtained. For steady and non-steady state forms of the LRT equation with force terms, similarity reductions are obtained via the classical symmetry analysis method. Both of the considered problems are not seen in the literature. The results obtained in this paper are new solutions and believed to have a major role in the development of the model.

scholarly journals Similarity Reductions and New Exact Solutions for B-Family Equations

2012 ◽  
Vol 2 (3) ◽  
pp. 40-43 ◽  
Author(s):  
G. M. Moatimid ◽  
M.H.M. Moussa ◽  
Rehab M. El-Shiekh ◽  
A. A. El-Satar
Keyword(s):  
Exact Solutions ◽  
New Exact Solutions ◽  
Similarity Reductions
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