scholarly journals On Truly Nonlinear Oscillator Equations of Ermakov-Pinney Type

2021 ◽  
Vol 19 (6) ◽  
pp. 970-983
Author(s):  
Marcellin Nonti ◽  
Kolawole Kegnide Damien Adjai ◽  
Jean Akande ◽  
Marc Delphin Monsia
Keyword(s):  
Differential Equations ◽  
Phase Plane ◽  
Elliptic Functions ◽  
Nonlinear Oscillators ◽  
Phase Plane Analysis ◽  
Exact Integration ◽  
Plane Analysis ◽  
Existence Of Periodic Solutions ◽  
First Time ◽  
Oscillator Equations

In this paper we present a general class of differential equations of Ermakov-Pinney type which may serve as truly nonlinear oscillators. We show the existence of periodic solutions by exact integration after the phase plane analysis. The related quadratic Lienard type equations are examined to show for the first time that the Jacobi elliptic functions may be solution of second-order autonomous non-polynomial differential equations.

Bifurcation analysis of the propagation of femtosecond pulses for the Triki-Biswas equation in monomode optical fibers

2019 ◽  
Vol 33 (29) ◽  
pp. 1950346 ◽  
Author(s):  
Asit Saha
Keyword(s):  
Optical Fibers ◽  
Bifurcation Analysis ◽  
Phase Plane ◽  
Dynamical Behavior ◽  
Phase Plane Analysis ◽  
Femtosecond Pulses ◽  
Plane Analysis ◽  
Solitary Pulse ◽  
Time Series Plot ◽  
First Time

Bifurcation analysis of the propagation of femtosecond pulses for the Triki–Biswas (TB) equation in monomode optical fibers is reported for the first time. Bifurcation of phase plots of the dynamical system is dispensed using phase plane analysis through symbolic computation. It is observed that the TB equation supports femtosecond solitary pulse, periodic pulse, superperiodic pulse, kink and anti-kink pulses, which are presented through time series plot numerically. Analytical forms of the femtosecond solitary pulses are obtained. This contribution may be applicable to interpret the dynamical behavior of various femtosecond pulses in monomode optical fibers beyond the Kerr limit.

A non-oscillation theorem for nonlinear differential equations with p-Laplacian

2006 ◽  
Vol 136 (3) ◽  
pp. 633-647 ◽  
Author(s):  
Jitsuro Sugie ◽  
Masakazu Onitsuka
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Asymptotic Behaviour ◽  
Linear Differential Equation ◽  
Phase Plane ◽  
Nonlinear Differential Equations ◽  
Phase Plane Analysis ◽  
Oscillation Theorem ◽  
Plane Analysis ◽  
Linear Differential

The equation considered in this paper is tp(φp(x′))′ + g(x) = 0, where φp(x′) = |x′|p−2x′ with p > 1, and g(x) satisfies the signum condition xg(x) > 0 if x ≠ 0 but is not assumed to be monotone. Our main objective is to establish a criterion on g(x) for all non-trivial solutions to be non-oscillatory. The criterion is the best possible. The method used here is the phase-plane analysis of a system equivalent to this differential equation. The asymptotic behaviour is also examined in detail for eventually positive solutions of a certain half-linear differential equation.

Whole-body phase plane analysis for standard maximum vertical jump assessment

2021 ◽  
Vol 90 ◽  
pp. 203-204
Author(s):  
C. Rodrigues ◽  
M. Correia ◽  
J. Abrantes ◽  
B. Rodrigues ◽  
J. Nadal
Keyword(s):  
Phase Plane ◽  
Vertical Jump ◽  
Whole Body ◽  
Phase Plane Analysis ◽  
Plane Analysis

scholarly journals Phase-plane analysis of driven multi-lane exclusion models

2012 ◽  
Vol 2012 (04) ◽  
pp. P04004 ◽  
Author(s):  
Vandana Yadav ◽  
Rajesh Singh ◽  
Sutapa Mukherji
Keyword(s):  
Phase Plane ◽  
Phase Plane Analysis ◽  
Plane Analysis

scholarly journals Subharmonic solutions of bounded coupled Hamiltonian systems with sublinear growth

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Fanfan Chen ◽  
Dingbian Qian ◽  
Xiying Sun ◽  
Yinyin Wu
Keyword(s):  
Hamiltonian Systems ◽  
Phase Plane ◽  
Phase Plane Analysis ◽  
Zero Eigenvalue ◽  
Subharmonic Solutions ◽  
Existence And Multiplicity ◽  
Plane Analysis ◽  
Higher Dimensional ◽  
Dimensional Version ◽  
Twist Theorem

<p style='text-indent:20px;'>We prove the existence and multiplicity of subharmonic solutions for bounded coupled Hamiltonian systems. The nonlinearities are assumed to satisfy Landesman-Lazer conditions at the zero eigenvalue, and to have some kind of sublinear behavior at infinity. The proof is based on phase plane analysis and a higher dimensional version of the Poincaré-Birkhoff twist theorem by Fonda and Ureña. The results obtained generalize the previous works for scalar second-order differential equations or relativistic equations to higher dimensional systems.</p>

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