This article describes the solution procedure of the fractional Pade-Ⅱ equation and generalized Zakharov equation(GSEs)using the sine-cosine method.Pade-Ⅱ is an important nonlinear wave equation modeling unidirectio...This article describes the solution procedure of the fractional Pade-Ⅱ equation and generalized Zakharov equation(GSEs)using the sine-cosine method.Pade-Ⅱ is an important nonlinear wave equation modeling unidirectional propagation of long-wave in dispersive media and GSEs are used to model the interaction between one-dimensional high,and low-frequency waves.Classes of trigonometric and hyperbolic function solutions in fractional calculus are discussed.Graphical simulations of the numerical solutions are flaunted by MATLAB.展开更多
It is challenging to predict the frequency property of a nonlinear vibration system conveniently and efficiently.Especially,an invalid or physically irrelevant result might be obtained by some advanced methods.Therefo...It is challenging to predict the frequency property of a nonlinear vibration system conveniently and efficiently.Especially,an invalid or physically irrelevant result might be obtained by some advanced methods.Therefore,predicting the frequency lacks an expedient and efficient method.This challenge is addressed by developing a straightforward and effective frequency formulation that reliably predicts the frequency-amplitude relationship.This study provides a one-step approach which can fast determine the periodic properties of any conservative oscillators and also provides a reference for other similar studies.展开更多
文摘This article describes the solution procedure of the fractional Pade-Ⅱ equation and generalized Zakharov equation(GSEs)using the sine-cosine method.Pade-Ⅱ is an important nonlinear wave equation modeling unidirectional propagation of long-wave in dispersive media and GSEs are used to model the interaction between one-dimensional high,and low-frequency waves.Classes of trigonometric and hyperbolic function solutions in fractional calculus are discussed.Graphical simulations of the numerical solutions are flaunted by MATLAB.
基金Natural Science Foundation of Shaanxi Provincial Department of Education in 2022,China(No.22JK0437)。
文摘It is challenging to predict the frequency property of a nonlinear vibration system conveniently and efficiently.Especially,an invalid or physically irrelevant result might be obtained by some advanced methods.Therefore,predicting the frequency lacks an expedient and efficient method.This challenge is addressed by developing a straightforward and effective frequency formulation that reliably predicts the frequency-amplitude relationship.This study provides a one-step approach which can fast determine the periodic properties of any conservative oscillators and also provides a reference for other similar studies.
