Modeling physical systems by effective harmonic oscillators: The optimized quadratic approximation

1995 ◽  
Vol 102 (8) ◽  
pp. 3337-3348 ◽  
Author(s):  
Jianshu Cao ◽  
Gregory A. Voth
Keyword(s):  
Quadratic Approximation ◽  
Harmonic Oscillators ◽  
Physical Systems ◽  
Modeling Physical Systems

scholarly journals Modeling Physical Systems

2020 ◽  
pp. 19-40
Author(s):  
Walid M. Taha ◽  
Abd-Elhamid M. Taha ◽  
Johan Thunberg
Keyword(s):  
Physical Systems ◽  
Modeling Physical Systems

Generalized Harmonic Oscillators: Velocity Dependent Frequencies

2001 ◽  
Author(s):  
Ronald E. Mickens
Keyword(s):  
Nonlinear Oscillator ◽  
First Integral ◽  
Harmonic Oscillators ◽  
System Of Equations ◽  
Research Grants ◽  
Physical Systems ◽  
New Class ◽  
Generalized Harmonic Oscillators ◽  
Special Cases ◽  
Oscillator Equations

Abstract Preliminary results are given on a new class of nonlinear oscillator equations that generalize those of the usual linear harmonic case. These equations take the form ẋ = f(x)y and ẏ = −g(y)x, where f(x) and g(y) are continuous with first derivatives, and f(0) > 0, g(0) > 0. Of interest is the fact that these equations have a first-integral, i.e., there exists a function H(x,y) such that along a particular trajectory in the (x,y) phase space, H(x,y) = constant. We work out several general results related to this system of equations and illustrate them with several special cases that correspond to models of physical systems. The work reported here was supported in part by research grants from DOE and the MBRS-SCORE Program at Clark Atlanta University.

scholarly journals Some Analytical Solitary Wave Solutions for the Generalized q-Deformed Sinh-Gordon Equation: ∂2θ/∂z∂ξ=αsinhq⁡(βθγ)p-δ

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
H. Eleuch
Keyword(s):  
Solitary Wave ◽  
Gordon Equation ◽  
Soliton Solutions ◽  
Solitary Wave Solutions ◽  
Physical Systems ◽  
Wave Solutions ◽  
Modeling Physical Systems

We introduce the generalized q-deformed Sinh-Gordon equation and derive analytical soliton solutions for some sets of parameters. This new defined equation could be useful for modeling physical systems with violated symmetries.

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