Time-periodic problem for a weakly nonlinear telegraph equation with directional derivative in the boundary condition

2015 ◽  
Vol 51 (10) ◽  
pp. 1369-1386 ◽  
Author(s):  
S. S. Kharibegashvili ◽  
O. M. Dzhokhadze
Keyword(s):  
Boundary Condition ◽  
Directional Derivative ◽  
Periodic Problem ◽  
Telegraph Equation ◽  
Weakly Nonlinear ◽  
Nonlinear Telegraph Equation ◽  
Time Periodic

Continuous symmetries of the discrete nonlinear telegraph equation

1999 ◽  
Vol 10 (3) ◽  
pp. 265-284 ◽  
Author(s):  
M. S. ODY ◽  
A. K. COMMON ◽  
M. I. SOBHY
Keyword(s):  
Initial Data ◽  
Difference Equations ◽  
Numerical Scheme ◽  
Telegraph Equation ◽  
Lie Symmetries ◽  
Discrete Equation ◽  
Symmetry Reductions ◽  
Nonlinear Telegraph Equation ◽  
Continuous Symmetries

The method of classical Lie symmetries, generalised to differential-difference equations by Quispel, Capel and Sahadevan, is applied to the discrete nonlinear telegraph equation. The symmetry reductions thus obtained are compared with analogous results for the continuous telegraph equation. Some of these ‘continuous’ reductions are used to provide initial data for a numerical scheme which attempts to solve the corresponding discrete equation.

Combined Parametrical and Transversal Excitation of a Stretched String in an Elastic Medium

2001 ◽  
Author(s):  
Caswita ◽  
A. H. P. van der Burgh
Keyword(s):  
Periodic Solutions ◽  
Elastic Medium ◽  
Integrodifferential Equation ◽  
Averaging Method ◽  
Telegraph Equation ◽  
Point Boundary ◽  
Time Periodic Solutions ◽  
The Stability ◽  
Two Parameters ◽  
Time Periodic

Abstract In this paper we consider a two-point boundary alue problem for an integrodifferential equation. This equation can be considered as a nonlinearly perturbed telegraph equation including both parametrical and transversal excitation. The attention will be focused on time-periodic solutions consisting of two modes. The first mode is generated by parametrical excitation and the second one is generated by vertical (transversal) excitation. This interaction of two modes can occur for special combinations of values of two parameters in the equation For the study of time-periodic solutions the averaging method will be used and the stability of the time-periodic solutions will be analyzed in linear approximation.

DISCRETE PROCEDURE OF OPTIMAL STABILIZATION FOR PERIODIC LINEAR SYSTEMS OF DIFFERENTIAL EQUATIONS

2018 ◽  
pp. 891-906
Author(s):  
Roman Ivanovich Shevchenko ◽  
Yuri Filippovich Dolgii
Keyword(s):  
Differential Equations ◽  
Discrete Time ◽  
Periodic Problem ◽  
Optimal Stabilization ◽  
Systems Of Differential Equations ◽  
Special Procedure ◽  
Periodic Linear ◽  
System States ◽  
Linear Periodic Systems ◽  
Time Periodic

We propose procedure to solve the optimal stabilization problem for linear periodic systems of differential equations. Stabilizing controls, formed as a feedback, are defined by the system states at the fixed instants of time. Equivalent discrete-time linear periodic problem of optimal stabilization is considered. We propose a special procedure for the solution of discrete periodic Riccati equation. We investigate the relation between continuous-time and discrete-time periodic optimal stabilization problems. The proposed method is used for stabilization of mechanical systems.

Local and nonlocal symmetries for nonlinear telegraph equation

2005 ◽  
Vol 46 (2) ◽  
pp. 023505 ◽  
Author(s):  
G. W. Bluman ◽  
Temuerchaolu ◽  
R. Sahadevan
Keyword(s):  
Telegraph Equation ◽  
Nonlocal Symmetries ◽  
Nonlinear Telegraph Equation
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