A new generalized F-expansion method is introduced and applied to the study of the （2＋1）-dimensional Boussinesq equation. The further extension of the method is discussed at the end of this paper.
In this paper, we employ the bifurcation method of dynamical systems to study the solitary waves and periodic waves of a generalized Boussinesq equations. All possible phase portraits in the parameter plane for the tr...In this paper, we employ the bifurcation method of dynamical systems to study the solitary waves and periodic waves of a generalized Boussinesq equations. All possible phase portraits in the parameter plane for the travelling wave systems are obtained. The possible solitary wave solutions, periodic wave solutions and cusp waves for the general Boussinesq type fluid model are also investigated.展开更多
A new general algebraic method is presented to uniformly construct a series of exact solutions for nonlinear evolution equations （NLEEs）. For illustration, we apply the new method to shallow long wave approximate eq...A new general algebraic method is presented to uniformly construct a series of exact solutions for nonlinear evolution equations （NLEEs）. For illustration, we apply the new method to shallow long wave approximate equations and successfully obtain abundant new exact solutions, which include rational solitary wave solutions and rational triangular periodic wave solutions. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in mathematical physics.展开更多
Based on a nonhydrostatic numerical ocean model developed by one of the authors, the interaction of an intemal solitary wave with a step-type topography was investigated. Over the step topography, the flow pattern cou...Based on a nonhydrostatic numerical ocean model developed by one of the authors, the interaction of an intemal solitary wave with a step-type topography was investigated. Over the step topography, the flow pattern could be classified into three categories： 1） the propagation and spatial structure of the internal solitary wave was little influenced by the bottom topography, 2） the internal solitary wave was significantly distorted by the blocking effect of the topography without the occurrence of wave breaking and 3） the internal solitary wave was broken as it encountered and passed over the bottom topography. A detailed description of the processes leading to wave breaking is given in this paper together with energy budget analysis. The results revealed that the maximum of the energy dissipation rate is no more than 40%, which is consistent with available experimental data.展开更多
基金The project supported by the Major Project of National Natural Science Foundation of China under Grant No. 49894190 and the Knowledge Innovation Project of CAS under Grant No. KZCXl-sw-18
文摘A new generalized F-expansion method is introduced and applied to the study of the （2＋1）-dimensional Boussinesq equation. The further extension of the method is discussed at the end of this paper.
基金The project supported by National Natural Science Foundation of China under Grant No. 10401022
文摘In this paper, we employ the bifurcation method of dynamical systems to study the solitary waves and periodic waves of a generalized Boussinesq equations. All possible phase portraits in the parameter plane for the travelling wave systems are obtained. The possible solitary wave solutions, periodic wave solutions and cusp waves for the general Boussinesq type fluid model are also investigated.
文摘A new general algebraic method is presented to uniformly construct a series of exact solutions for nonlinear evolution equations （NLEEs）. For illustration, we apply the new method to shallow long wave approximate equations and successfully obtain abundant new exact solutions, which include rational solitary wave solutions and rational triangular periodic wave solutions. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in mathematical physics.
基金This work was financially supported by the National Natural Science Foundation of China(40576010).
文摘Based on a nonhydrostatic numerical ocean model developed by one of the authors, the interaction of an intemal solitary wave with a step-type topography was investigated. Over the step topography, the flow pattern could be classified into three categories： 1） the propagation and spatial structure of the internal solitary wave was little influenced by the bottom topography, 2） the internal solitary wave was significantly distorted by the blocking effect of the topography without the occurrence of wave breaking and 3） the internal solitary wave was broken as it encountered and passed over the bottom topography. A detailed description of the processes leading to wave breaking is given in this paper together with energy budget analysis. The results revealed that the maximum of the energy dissipation rate is no more than 40%, which is consistent with available experimental data.
