scholarly journals Discrete Symmetry Transformations of Third Order Ordinary Differential Equations and Applications

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Discrete Symmetries ◽  
Discrete Symmetry ◽  
Third Order ◽  
Symmetry Transformations ◽  
Paper List

Third order ordinary differential equations have already been classified by the Lie algebra they admit. Invariant equations corresponding to these Lie algebras are also available in the literature [17]. In this paper, list of all discrete symmetries corresponding to these invariant ordinary differential equations, are obtained. Some particular examples are given to show the significance of the work.

scholarly journals Symmetry Reductions, Exact Solutions, and Conservation Laws of a Modified Hunter-Saxton Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Andrew Gratien Johnpillai ◽  
Chaudry Masood Khalique
Keyword(s):  
Differential Equations ◽  
Conservation Laws ◽  
Ordinary Differential Equations ◽  
Lie Algebra ◽  
Point Of View ◽  
Third Order ◽  
Theoretic Point ◽  
Group Invariant Solutions ◽  
Nonlocal Conservation Laws ◽  
Symmetry Generators

We study a modified Hunter-Saxton equation from the Lie group-theoretic point of view. The Lie point symmetry generators of the underlying equation are derived. We utilize the Lie algebra admitted by the equation to obtain the optimal system of one-dimensional subalgebras of the Lie algebra of the equation. These subalgebras are then used to reduce the underlying equation to nonlinear third-order ordinary differential equations. Exact traveling wave group-invariant solutions for the equation are constructed by integrating the reduced ordinary differential equations. Moreover, using the variational method, we construct infinite number of nonlocal conservation laws by the transformation of the dependent variable of the underlying equation.

Boundary-Value Problems for Third-Order Lipschitz Ordinary Differential Equations

2014 ◽  
Vol 58 (1) ◽  
pp. 183-197 ◽  
Author(s):  
John R. Graef ◽  
Johnny Henderson ◽  
Rodrica Luca ◽  
Yu Tian
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Optimal Length ◽  
The Third

AbstractFor the third-order differential equationy′″ = ƒ(t, y, y′, y″), where, questions involving ‘uniqueness implies uniqueness’, ‘uniqueness implies existence’ and ‘optimal length subintervals of (a, b) on which solutions are unique’ are studied for a class of two-point boundary-value problems.

Determination of Nonchaotic Behavior for Some Classes of Polynomial Jerk Equations

2020 ◽  
Vol 30 (08) ◽  
pp. 2050117
Author(s):  
Marcelo Messias ◽  
Rafael Paulino Silva
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Simple Form ◽  
Chaotic Dynamics ◽  
Third Order ◽  
Algebraic Criterion

In this work, by using an algebraic criterion presented by us in an earlier paper, we determine the conditions on the parameters in order to guarantee the nonchaotic behavior for some classes of nonlinear third-order ordinary differential equations of the form [Formula: see text] called jerk equations, where [Formula: see text] is a polynomial of degree [Formula: see text]. This kind of equation is often used in literature to study chaotic dynamics, due to its simple form and because it appears as mathematical model in several applied problems. Hence, it is an important matter to determine when it is chaotic and also nonchaotic. The results stated here, which are proved using the mentioned algebraic criterion, corroborate and extend some results already presented in literature, providing simpler proofs for the nonchaotic behavior of certain jerk equations. The algebraic criterion proved by us is quite general and can be used to study nonchaotic behavior of other types of ordinary differential equations.

Sign in / Sign up

Export Citation Format

Share Document