The generalized Duffing oscillator

•The generalized Duffing oscillator is considered.•The Painleve test is used to study the integrability of equations.•The exact solutions in the form of periodic oscillations and solitary pulse are given. A generalized Duffing oscillator is considered, which takes into account high-order derivatives...

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Bibliographic Details
Published in:Communications in nonlinear science & numerical simulation Vol. 93; p. 105526
Main Author: Kudryashov, Nikolay A.
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.02.2021
Elsevier Science Ltd
Subjects:
Algorithms
Constants
Differential equations
Duffing oscillator
Duffing oscillators
Exact solution
Exact solutions
Integral calculus
Nonlinear equations
Oscillators
Painlevé test
Periodic oscillations
Duffing oscillator
Periodic oscillations
Painlevé test
Exact solution
ISSN:1007-5704, 1878-7274
Online Access:Get full text
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Summary:•The generalized Duffing oscillator is considered.•The Painleve test is used to study the integrability of equations.•The exact solutions in the form of periodic oscillations and solitary pulse are given. A generalized Duffing oscillator is considered, which takes into account high-order derivatives and power nonlinearities. The Painlevé test is applied to study the integrability of the mathematical model. It is shown that the generalized Duffing oscillator passes the Painlevé test only in the case of the classic Duffing oscillator which is described by the second-order differential equation. However, in the general case there are the expansion of the general solution in the Laurent series with two arbitrary constants. This allows us to search for exact solutions of generalized Duffing oscillators with two arbitrary constants using the classical Duffing oscillator as the simplest equation. The algorithm of finding exact solutions is presented. Exact solutions for the generalized Duffing oscillator are found for equations of fourth, sixth, eighth and tenth order in the form of periodic oscillations and solitary pulse.
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ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2020.105526