A Simple Method to Obtain First Integrals of Dynamical Systems

1991 ◽  
pp. 125-128
Author(s):  
R. Conte ◽  
M. Musette
Keyword(s):  
Dynamical Systems ◽  
First Integrals ◽  
Simple Method

Symmetries, first integrals and splittability of dynamical systems

1978 ◽  
Vol 21 (7) ◽  
pp. 253-257 ◽  
Author(s):  
F. González-Gascón ◽  
F. Moreno-Insertis
Keyword(s):  
Dynamical Systems ◽  
First Integrals

scholarly journals Travelling-Wave Solutions for Wave Equations with Two Exponential Nonlinearities

2018 ◽  
Vol 73 (10) ◽  
pp. 883-892
Author(s):  
Stefan C. Mancas ◽  
Haret C. Rosu ◽  
Maximino Pérez-Maldonado
Keyword(s):  
Dynamical Systems ◽  
Elliptic Equations ◽  
Hypergeometric Functions ◽  
Wave Equations ◽  
Constant Term ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Simple Method ◽  
Solutions Of Wave Equations ◽  
Wave Solutions

AbstractWe use a simple method that leads to the integrals involved in obtaining the travelling-wave solutions of wave equations with one and two exponential nonlinearities. When the constant term in the integrand is zero, implicit solutions in terms of hypergeometric functions are obtained, while when that term is nonzero, all the basic travelling-wave solutions of Liouville, Tzitzéica, and their variants, as as well sine/sinh-Gordon equations with important applications in the phenomenology of nonlinear physics and dynamical systems are found through a detailed study of the corresponding elliptic equations.

TRACKING SUSTAINED CHAOS

2000 ◽  
Vol 10 (03) ◽  
pp. 571-578 ◽  
Author(s):  
IRA B. SCHWARTZ ◽  
IOANA TRIANDAF
Keyword(s):  
Dynamical Systems ◽  
Simple Method ◽  
Periodically Driven ◽  
Unstable Solutions ◽  
Chaotic Transients ◽  
Parameter Values

Tracking unstable periodic states first introduced in [Schwartz & Triandaf, 1992] is the process of continuing unstable solutions as a systems parameter is varied in experiments. The tracked dynamical objects have been periodic saddles of well-defined finite periods. However, other saddles, such as chaotic saddles, have not been successfully "tracked," or continued. In this paper, we introduce a new yet simple method which can be used to track chaotic saddles in dynamical systems, which allows an experimentalist to sustain chaotic transients far away from crisis parameter values. The method is illustrated on a periodically driven CO 2 laser.

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