Symmetry groups, conservation laws and group-invariant solutions of the Marguerre-von Kármán equations

2019 ◽  
pp. 338-343
Author(s):  
V. Vassilev
Keyword(s):  
Conservation Laws ◽  
Symmetry Groups ◽  
Invariant Solutions ◽  
Group Invariant ◽  
Von Karman ◽  
Von Kármán Equations ◽  
Group Invariant Solutions ◽  
Von Kármán

scholarly journals Reductions and conservation laws for BBM and modified BBM equations

2016 ◽  
Vol 14 (1) ◽  
pp. 1138-1148
Author(s):  
Maryam Khorshidi ◽  
Mehdi Nadjafikhah ◽  
Hossein Jafari ◽  
Maysaa Al Qurashi
Keyword(s):  
Conservation Laws ◽  
Lie Algebras ◽  
Adjoint Representation ◽  
Differential Invariants ◽  
Symmetry Groups ◽  
Invariant Solutions ◽  
Group Invariant ◽  
New Exact Solutions ◽  
Symmetry Properties ◽  
Group Invariant Solutions

AbstractIn this paper, the classical Lie theory is applied to study the Benjamin-Bona-Mahony (BBM) and modified Benjamin-Bona-Mahony equations (MBBM) to obtain their symmetries, invariant solutions, symmetry reductions and differential invariants. By observation of the the adjoint representation of Mentioned symmetry groups on their Lie algebras, we find the primary classification (optimal system) of their group-invariant solutions which provides new exact solutions to BBM and MBBM equations. Finally, conservation laws of the BBM and MBBM equations are presented. Some aspects of their symmetry properties are given too.

scholarly journals Symmetry Reductions of (2 + 1)-Dimensional CDGKS Equation and Its Reduced Lax Pairs

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Na Lv ◽  
Xuegang Yuan ◽  
Jinzhi Wang
Keyword(s):  
Direct Method ◽  
Lax Pair ◽  
Group Method ◽  
Symmetry Groups ◽  
Invariant Solutions ◽  
Lax Pairs ◽  
Group Invariant ◽  
Lie Group Method ◽  
Group Invariant Solutions ◽  
Symmetry Transformations

With the aid of symbolic computation, we obtain the symmetry transformations of the (2 + 1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada (CDGKS) equation by Lou’s direct method which is based on Lax pairs. Moreover, we use the classical Lie group method to seek the symmetry groups of both the CDGKS equation and its Lax pair and then reduce them by the obtained symmetries. In particular, we consider the reductions of the Lax pair completely. As a result, three reduced (1 + 1)-dimensional equations with their new Lax pairs are presented and some group-invariant solutions of the equation are given.

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