The generalized Duffing oscillator

被引：67

作者：

Kudryashov, Nikolay A. ^{[1
]}

机构：

[1] Natl Res Nucl Univ MEPhI, Moscow Engn Phys Inst, 31 Kashirskoe Shosse, Moscow 115409, Russia

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2021年 / 93卷 / 93期

基金：

俄罗斯科学基金会;

关键词：

Duffing oscillator; Painlevetest; Exact solution; Periodic oscillations; DISPERSIVE OPTICAL SOLITONS; KERR LAW NONLINEARITY; QUINTIC-SEPTIC LAW; DIFFERENTIAL-EQUATIONS; SIMPLEST EQUATION; LOGISTIC FUNCTION; SOLITARY WAVES;

D O I：

10.1016/j.cnsns.2020.105526

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A generalized Duffing oscillator is considered, which takes into account high-order derivatives and power nonlinearities. The Painlevetest is applied to study the integrability of the mathematical model. It is shown that the generalized Duffing oscillator passes the Painlevetest 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. (C) 2020 Elsevier B.V. All rights reserved.

引用

页数：16

共 53 条

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