scholarly journals Mei Symmetry and Conservation Laws for Time-Scale Nonshifted Hamilton Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Yi Zhang
Keyword(s):  
Phase Space ◽  
Conservation Laws ◽  
Time Scale ◽  
Symmetry And Conservation Laws ◽  
Dynamic Equations ◽  
Constrained Mechanical Systems ◽  
Hamilton Principle ◽  
Hamilton Equations ◽  
Mei Symmetry ◽  
Case Based

The Mei symmetry and conservation laws for time-scale nonshifted Hamilton equations are explored, and the Mei symmetry theorem is presented and proved. Firstly, the time-scale Hamilton principle is established and extended to the nonconservative case. Based on the Hamilton principles, the dynamic equations of time-scale nonshifted constrained mechanical systems are derived. Secondly, for the time-scale nonshifted Hamilton equations, the definitions of Mei symmetry and their criterion equations are given. Thirdly, Mei symmetry theorems are proved, and the Mei-type conservation laws in time-scale phase space are driven. Two examples show the validity of the results.

scholarly journals Mei Symmetry and New Conserved Quantities of Time-Scale Birkhoff’s Equations

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Xiang-Hua Zhai ◽  
Yi Zhang
Keyword(s):  
Hamiltonian System ◽  
Time Scales ◽  
Time Scale ◽  
Dynamic Equations ◽  
Conserved Quantities ◽  
Dynamical Processes ◽  
Birkhoffian System ◽  
Special Case ◽  
Mei Symmetry

The time-scale dynamic equations play an important role in modeling complex dynamical processes. In this paper, the Mei symmetry and new conserved quantities of time-scale Birkhoff’s equations are studied. The definition and criterion of the Mei symmetry of the Birkhoffian system on time scales are given. The conditions and forms of new conserved quantities which are found from the Mei symmetry of the system are derived. As a special case, the Mei symmetry of time-scale Hamilton canonical equations is discussed and new conserved quantities for the Hamiltonian system on time scales are derived. Two examples are given to illustrate the application of results.

Time-Scale Version of Generalized Birkhoffian Mechanics and Its Symmetries and Conserved Quantities of Noether Type

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Jin-Yue Chen ◽  
Yi Zhang
Keyword(s):  
Conservation Laws ◽  
Time Scales ◽  
Time Scale ◽  
Symmetry And Conservation Laws ◽  
Conserved Quantity ◽  
Noether Symmetry ◽  
Conserved Quantities ◽  
Birkhoffian System

The time-scale version of Noether symmetry and conservation laws for three Birkhoffian mechanics, namely, nonshifted Birkhoffian systems, nonshifted generalized Birkhoffian systems, and nonshitfed constrained Birkhoffian systems, are studied. Firstly, on the basis of the nonshifted Pfaff-Birkhoff principle on time scales, Birkhoff’s equations for nonshifted variables are deduced; then, Noether’s quasi-symmetry for the nonshifted Birkhoffian system is proved and time-scale conserved quantity is presented. Secondly, the nonshifted generalized Pfaff-Birkhoff principle on time scales is proposed, the generalized Birkhoff’s equations for nonshifted variables are derived, and Noether’s symmetry for the nonshifted generalized Birkhoffian system is established. Finally, for the nonshifted constrained Birkhoffian system, Noether’s symmetry and time-scale conserved quantity are proposed and proved. The validity of the result is proved by examples.

scholarly journals On Galilean Invariant and Energy Preserving BBM-Type Equations

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 878
Author(s):  
Alexei Cheviakov ◽  
Denys Dutykh ◽  
Aidar Assylbekuly
Keyword(s):  
Wave Equation ◽  
Conservation Laws ◽  
Numerical Simulations ◽  
Solitary Waves ◽  
Local Symmetry ◽  
Symmetry And Conservation Laws ◽  
Higher Order ◽  
Special Equation ◽  
Long Wave ◽  
Local Symmetries

We investigate a family of higher-order Benjamin–Bona–Mahony-type equations, which appeared in the course of study towards finding a Galilei-invariant, energy-preserving long wave equation. We perform local symmetry and conservation laws classification for this family of Partial Differential Equations (PDEs). The analysis reveals that this family includes a special equation which admits additional, higher-order local symmetries and conservation laws. We compute its solitary waves and simulate their collisions. The numerical simulations show that their collision is elastic, which is an indication of its S−integrability. This particular PDE turns out to be a rescaled version of the celebrated Camassa–Holm equation, which confirms its integrability.

scholarly journals Symmetry and conservation laws in non-holonomic mechanics

2021 ◽  
Vol 62 (5) ◽  
pp. 052901
Author(s):  
Enrico Massa ◽  
Enrico Pagani
Keyword(s):  
Conservation Laws ◽  
Symmetry And Conservation Laws

scholarly journals Existence of positive periodic solutions for nonlinear neutral dynamic equations with variable coefficients on a time scale

2018 ◽  
Vol 36 (2) ◽  
pp. 185
Author(s):  
Abdelouaheb Ardjouni ◽  
Ahcene Djoudi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Time Scale ◽  
Variable Coefficients ◽  
Dynamic Equations ◽  
Positive Periodic Solutions ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Neutral Dynamic Equations ◽  
Compact Map

Let T be a periodic time scale. The purpose of this paper is to use Krasnoselskii's fixed point theorem to prove the existence of positive periodic solutions for nonlinear neutral dynamic equations with variable coefficients on a time scale. We invert these equations to construct a sum of a contraction and a compact map which is suitable for applying the Krasnoselskii's theorem. The results obtained here extend the work of Candan <cite>c1</cite>.

scholarly journals Oscillation Criteria for Second Order Impulsive Delay Dynamic Equations on Time Scale

2021 ◽  
Vol 45 (4) ◽  
pp. 531-542
Author(s):  
GOKULA NANDA CHHATRIA ◽  
Keyword(s):  
Time Scale ◽  
Second Order ◽  
Dynamic Equations ◽  
Riccati Transformation ◽  
Transformation Technique ◽  
Oscillation Criteria ◽  
Delay Dynamic Equations ◽  
Impulsive Delay

In this work, we study the oscillation of a kind of second order impulsive delay dynamic equations on time scale by using impulsive inequality and Riccati transformation technique. Some examples are given to illustrate our main results.

scholarly journals Oscillation for nonlinear second order dynamic equations on a time scale

2005 ◽  
Vol 301 (2) ◽  
pp. 491-507 ◽  
Author(s):  
Martin Bohner ◽  
Lynn Erbe ◽  
Allan Peterson
Keyword(s):  
Time Scale ◽  
Second Order ◽  
Dynamic Equations
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