This paper investigates the orbital stability of periodic traveling wave solutions to the generalized Zakharov equations {iu ＋uxx = uv ＋ ｜u｜^2u, vtt-vxx=（｜u｜^2）xx.First, we prove the existence of a smooth c...This paper investigates the orbital stability of periodic traveling wave solutions to the generalized Zakharov equations {iu ＋uxx = uv ＋ ｜u｜^2u, vtt-vxx=（｜u｜^2）xx.First, we prove the existence of a smooth curve of positive traveling wave solutions of dnoidal type with a fixed fundamental period L for the generalized Zakharov equations. Then, by using the classical method proposed by Benjamin, Bona et al., we show that this solution is orbitally stable by perturbations with period L. The results on the orbital stability of periodic traveling wave solutions for the generalized Zakharov equations in this paper can be regarded as a perfect extension of the results of [15, 16, 19].展开更多
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
The existence and uniqueness of a global smooth solution of the initial value problem for a class of systems of multi-dimensional generalized Zakharov tyhe equations have been proved by means of a priori integral esti...The existence and uniqueness of a global smooth solution of the initial value problem for a class of systems of multi-dimensional generalized Zakharov tyhe equations have been proved by means of a priori integral estimates and Galerkin method.展开更多
基金supported by the National Natural Science Foundation of China(11401122)Science and technology project of Qufu Normal University(xkj201607)
文摘This paper investigates the orbital stability of periodic traveling wave solutions to the generalized Zakharov equations {iu ＋uxx = uv ＋ ｜u｜^2u, vtt-vxx=（｜u｜^2）xx.First, we prove the existence of a smooth curve of positive traveling wave solutions of dnoidal type with a fixed fundamental period L for the generalized Zakharov equations. Then, by using the classical method proposed by Benjamin, Bona et al., we show that this solution is orbitally stable by perturbations with period L. The results on the orbital stability of periodic traveling wave solutions for the generalized Zakharov equations in this paper can be regarded as a perfect extension of the results of [15, 16, 19].
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.
文摘The existence and uniqueness of a global smooth solution of the initial value problem for a class of systems of multi-dimensional generalized Zakharov tyhe equations have been proved by means of a priori integral estimates and Galerkin method.
