scholarly journals Numerical simulation of Harry Dym equation

2019 ◽  
Author(s):  
T. R. Ramesh Rao
Keyword(s):  
Numerical Simulation ◽  
Dym Equation ◽  
Harry Dym Equation

scholarly journals Self-Adjointness and Conservation Laws of Frobenius Type Equations

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 1987
Author(s):  
Haifeng Wang ◽  
Yufeng Zhang
Keyword(s):  
Conservation Laws ◽  
Burgers Equation ◽  
Kdv Equation ◽  
The Self ◽  
Kp Equation ◽  
Commutative Subalgebra ◽  
Kompaneets Equation ◽  
Dym Equation ◽  
Harry Dym Equation

The Frobenius KDV equation and the Frobenius KP equation are introduced, and the Frobenius Kompaneets equation, Frobenius Burgers equation and Frobenius Harry Dym equation are constructed by taking values in a commutative subalgebra Z2ε in the paper. The five equations are selected as examples to help us study the self-adjointness of Frobenius type equations, and we show that the first two equations are quasi self-adjoint and the last three equations are nonlinear self-adjointness. It follows that we give the symmetries of the Frobenius KDV and the Frobenius KP equation in order to construct the corresponding conservation laws.

scholarly journals The generalized Harry Dym equation

2003 ◽  
Vol 317 (3-4) ◽  
pp. 260-264 ◽  
Author(s):  
Ziemowit Popowicz
Keyword(s):  
Dym Equation ◽  
Harry Dym Equation

scholarly journals Approximate Symmetries of the Harry Dym Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Mehdi Nadjafikhah ◽  
Parastoo Kabi-Nejad
Keyword(s):  
Lie Algebra ◽  
Optimal System ◽  
Differential Invariants ◽  
Approximate Symmetries ◽  
One Dimensional ◽  
First Order ◽  
Optimal System Of Subalgebras ◽  
Dym Equation ◽  
The One ◽  
Harry Dym Equation

We derive the first-order approximate symmetries for the Harry Dym equation by the method of approximate transformation groups proposed by Baikov et al. (1989, 1996). Moreover, we investigate the structure of the Lie algebra of symmetries of the perturbed Harry Dym equation. We compute the one-dimensional optimal system of subalgebras as well as point out some approximately differential invariants with respect to the generators of Lie algebra and optimal system.

Sign in / Sign up

Export Citation Format

Share Document