scholarly journals Direct similarity reductions and new exact solutions of the short pulse equation

2019 ◽  
Vol 4 (2) ◽  
pp. 231-241 ◽  
Author(s):  
Quting Chen ◽  
◽  
Yadong Shang
Keyword(s):  
Exact Solutions ◽  
Short Pulse ◽  
New Exact Solutions ◽  
Short Pulse Equation ◽  
Similarity Reductions

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

Novel exact solutions to the short pulse equation

2010 ◽  
Vol 215 (11) ◽  
pp. 3899-3905 ◽  
Author(s):  
Zuntao Fu ◽  
Zhe Chen ◽  
Linna Zhang ◽  
Jiangyu Mao ◽  
Shikuo Liu
Keyword(s):  
Exact Solutions ◽  
Short Pulse ◽  
Short Pulse Equation

On exact solutions of the Schäfer–Wayne short pulse equation: WKI eigenvalue problem

2007 ◽  
Vol 40 (21) ◽  
pp. 5585-5596 ◽  
Author(s):  
Kuetche Kamgang Victor ◽  
Bouetou Bouetou Thomas ◽  
Timoleon Crepin Kofane
Keyword(s):  
Eigenvalue Problem ◽  
Exact Solutions ◽  
Short Pulse ◽  
Short Pulse Equation

New exact solutions of the Boussinesq equation

1990 ◽  
Vol 1 (3) ◽  
pp. 279-300 ◽  
Author(s):  
Peter A. Clarkson
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Ordinary Differential Equations ◽  
Boussinesq Equation ◽  
Painlevé Equations ◽  
Painleve Equations ◽  
New Exact Solutions ◽  
New Space ◽  
Manipulation Language ◽  
Similarity Reductions

In this paper new exact solutions are derived for the physically and mathematically significant Boussinesq equation. These are obtained in two different ways: first, by generating exact solutions to the ordinary differential equations which arise from (classical and nonclassical) similarity reductions of the Boussinesq equation (these ordinary differential equations are solvable in terms of the first, second and fourth Painlevé equations); and second, by deriving new space-independent similarity reductions of the Boussinesq equation. Extensive sets of exact solutions for both the second and fourth Painlevé equations are also generated. The symbolic manipulation language MACSYMA is employed to facilitate the calculations involved.

Analytic study of solutions for a two-component Novikov system

2020 ◽  
pp. 2150025
Author(s):  
Hui Gao ◽  
Gangwei Wang
Keyword(s):  
Exact Solutions ◽  
Stationary Solutions ◽  
Invariant Solutions ◽  
Group Invariant ◽  
New Exact Solutions ◽  
Two Component ◽  
Group Invariant Solutions ◽  
Symmetry Transformations ◽  
Symmetry Method ◽  
Similarity Reductions

Under investigation in this paper is a two-component Novikov system (also called Geng-Xue equation), which was proposed by Geng and Xue in 2009. Firstly, via the Lie symmetry method, infinitesimal generators, commutator table of Lie algebra and symmetry groups of the two-component Novikov system are presented. At the same time, some group invariant solutions are computed through similarity reductions. In particular, we construct peakon solution by applying the distribution theory. In addition, based on obtained group invariant solutions and symmetry transformations, we derive some new exact solutions, which include stationary solutions, smooth solutions, and a weak solution. The analytical properties to some of group invariant solutions and new exact solutions are discussed, such as decay, asymptotic behavior, and boundedness.

Exact Solutions to Short Pulse Equation

2009 ◽  
Vol 51 (3) ◽  
pp. 395-396 ◽  
Author(s):  
Fu Zun-Tao ◽  
Zheng Ming-Hua ◽  
Liu Shi-Kuo
Keyword(s):  
Exact Solutions ◽  
Short Pulse ◽  
Short Pulse Equation
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