In this paper, the nonlinear waves and their barotropic stability in the tropical ocean and atmosphere are studied with the qualitative theory of the ordinary differential equation. The relationship is derived between...In this paper, the nonlinear waves and their barotropic stability in the tropical ocean and atmosphere are studied with the qualitative theory of the ordinary differential equation. The relationship is derived between the stability of nonlinear waves with different frequencies and the basic currents and their horizontal shear in the tropical ocean and atmosphere.展开更多
A simple model of three coupled oscillators as an approximation of main modes behaviors in a spatial extended system is proposed. Multi-looping generalized synchronization and drift intermittent lag phase synchronizat...A simple model of three coupled oscillators as an approximation of main modes behaviors in a spatial extended system is proposed. Multi-looping generalized synchronization and drift intermittent lag phase synchronization phenomena are found in this simple model. For a certain of parameters in which chaotic-like intermittent behavior exhibit the amplitudes and phases of three modes are controlled to be synchronized states via coupling them with an external periodic mode.展开更多
By using the second-order potential theory proposed by the author, in this paper it is investigated that nonlinear interaction of P- and SV- waves in isotropic elastic media. It is pointed out that if the angle betwee...By using the second-order potential theory proposed by the author, in this paper it is investigated that nonlinear interaction of P- and SV- waves in isotropic elastic media. It is pointed out that if the angle between the vectors of both waves is close to the 'splitting angle',the weak segment in media may be splitted out. When the frequencies of two primary waves are different, only sum-frequency component of the interacting wave can cause the phenomenon above mentioned.展开更多
We show that the scattering operator carries a band in H^s (R^n)×H^(s-1)(R^n) into H^s (R^n)× H^(s-1)(R^n) for the sinh-Gordon equation and an analogous result also holds true for the nonlinear Schrdinger eq...We show that the scattering operator carries a band in H^s (R^n)×H^(s-1)(R^n) into H^s (R^n)× H^(s-1)(R^n) for the sinh-Gordon equation and an analogous result also holds true for the nonlinear Schrdinger equation with an exponential nonlinearity, where s≥n/2 is arbitrary and n≥2. Therefore, the scattering operators are infinitely smooth for the above two equations.展开更多
文摘In this paper, the nonlinear waves and their barotropic stability in the tropical ocean and atmosphere are studied with the qualitative theory of the ordinary differential equation. The relationship is derived between the stability of nonlinear waves with different frequencies and the basic currents and their horizontal shear in the tropical ocean and atmosphere.
文摘A simple model of three coupled oscillators as an approximation of main modes behaviors in a spatial extended system is proposed. Multi-looping generalized synchronization and drift intermittent lag phase synchronization phenomena are found in this simple model. For a certain of parameters in which chaotic-like intermittent behavior exhibit the amplitudes and phases of three modes are controlled to be synchronized states via coupling them with an external periodic mode.
文摘By using the second-order potential theory proposed by the author, in this paper it is investigated that nonlinear interaction of P- and SV- waves in isotropic elastic media. It is pointed out that if the angle between the vectors of both waves is close to the 'splitting angle',the weak segment in media may be splitted out. When the frequencies of two primary waves are different, only sum-frequency component of the interacting wave can cause the phenomenon above mentioned.
基金Supported by the National Natural Science Foundation of China. Grant 19901007.
文摘We show that the scattering operator carries a band in H^s (R^n)×H^(s-1)(R^n) into H^s (R^n)× H^(s-1)(R^n) for the sinh-Gordon equation and an analogous result also holds true for the nonlinear Schrdinger equation with an exponential nonlinearity, where s≥n/2 is arbitrary and n≥2. Therefore, the scattering operators are infinitely smooth for the above two equations.
