Ansatz method and the theory of dynamical systems are used to study the traveling wave solutions for the generalized Drinfeld-Sokolov equations. Under two groups of the parametric conditions, more solitary wave soluti...Ansatz method and the theory of dynamical systems are used to study the traveling wave solutions for the generalized Drinfeld-Sokolov equations. Under two groups of the parametric conditions, more solitary wave solutions, kink and anti-kink wave solutions and periodic wave solutions are obtained. Exact explicit parametric representations of these travelling wave solutions are given.展开更多
The simplified modified Camassa-Holm (SMCH) equation is an important nonlinear model equation for identifying various wave phenomena in ocean engineering and science. The new auxiliary equation (NAE) method has been a...The simplified modified Camassa-Holm (SMCH) equation is an important nonlinear model equation for identifying various wave phenomena in ocean engineering and science. The new auxiliary equation (NAE) method has been applied to the SMCH equation. Base on the method, we have obtained some novel an- alytical solutions such as hyperbolic, trigonometric, exponential, and rational function solutions of the SMCH equation. For appropriate values of parameters, three dimensional (3D) and two dimensional (2D) graphs are designed by Mathematica. The stability of the model is also discussed in this manuscript. The dynamic and physical behaviors of the solutions derived from the SMCH equation have been ex- tensively discussed by these plots. All our solutions are indispensable for understanding the nonlinear phenomena of dispersive waves that are important in ocean engineering and science. In addition, our results are essential to clarify the various oceanographic applications containing ocean gravity waves, offshore rig in water, energy associated with a moving ocean wave and numerous other related phenom- ena. Finally, the obtained solutions are helpful for studying wave interactions in many new structures and high-dimensional models.展开更多
In parametrically excited Faraday experiment the non-propagating solitons-breathers, kinksand breather pairs-have been observed at the interface of two insoluble liquids with different densities.Phenomena observed at ...In parametrically excited Faraday experiment the non-propagating solitons-breathers, kinksand breather pairs-have been observed at the interface of two insoluble liquids with different densities.Phenomena observed at the interface are similar to those on the surface, except that the eigenfrequencies are remarkably red-shifted, and the wave forms are flatter and less stable due to the presence of the upper liquid. A nonlinear Schrodinger equation with damping and drive terms has been derived to explain the new observations. Both experiment and theory show that the free surface wave is a special case of the interface wave.展开更多
With the aid of a class of nonlinear ordinary differential equation （ODE） and its various positive solutions, four types of exact solutions of the generalized derivative nonlinear Sehrodinger equation （GDNLSE） hav...With the aid of a class of nonlinear ordinary differential equation （ODE） and its various positive solutions, four types of exact solutions of the generalized derivative nonlinear Sehrodinger equation （GDNLSE） have been found out, which are the bell-type solitary wave solution, the algebraic solitary wave solution, the kink-type solitary wave solution and the sinusoidal traveling wave solution, provided that the coefficients of GDNLSE satisfy certain constraint conditions. For more general GDNLSE, the similar results are also given.展开更多
In this paper, the modified extended tanh method is used to construct more general exact solutions of a （2＋1）-dimensional nonlinear SchrSdinger equation. With the aid of Maple and Matlab software, we obtain exact e...In this paper, the modified extended tanh method is used to construct more general exact solutions of a （2＋1）-dimensional nonlinear SchrSdinger equation. With the aid of Maple and Matlab software, we obtain exact explicit kink wave solutions, peakon wave solutions, periodic wave solutions and their 3D images.展开更多
The generalized nonlinear Schrdinger equation with parabolic law nonlinearity is studied by using the factorization technique and the method of dynamical systems.From a dynamic point of view,the existence of smooth so...The generalized nonlinear Schrdinger equation with parabolic law nonlinearity is studied by using the factorization technique and the method of dynamical systems.From a dynamic point of view,the existence of smooth solitary wave,kink and anti-kink wave is proved and the sufficient conditions to guarantee the existence of the above solutions in different regions of the parametric space are given.Also,all possible explicit exact parametric representations of the waves are presented.展开更多
基金Project supported by the Key Project of Science Research Foundation of Educational Department of Yunnan Province, China (No.5Z0071A)
文摘Ansatz method and the theory of dynamical systems are used to study the traveling wave solutions for the generalized Drinfeld-Sokolov equations. Under two groups of the parametric conditions, more solitary wave solutions, kink and anti-kink wave solutions and periodic wave solutions are obtained. Exact explicit parametric representations of these travelling wave solutions are given.
文摘The simplified modified Camassa-Holm (SMCH) equation is an important nonlinear model equation for identifying various wave phenomena in ocean engineering and science. The new auxiliary equation (NAE) method has been applied to the SMCH equation. Base on the method, we have obtained some novel an- alytical solutions such as hyperbolic, trigonometric, exponential, and rational function solutions of the SMCH equation. For appropriate values of parameters, three dimensional (3D) and two dimensional (2D) graphs are designed by Mathematica. The stability of the model is also discussed in this manuscript. The dynamic and physical behaviors of the solutions derived from the SMCH equation have been ex- tensively discussed by these plots. All our solutions are indispensable for understanding the nonlinear phenomena of dispersive waves that are important in ocean engineering and science. In addition, our results are essential to clarify the various oceanographic applications containing ocean gravity waves, offshore rig in water, energy associated with a moving ocean wave and numerous other related phenom- ena. Finally, the obtained solutions are helpful for studying wave interactions in many new structures and high-dimensional models.
基金Project supported by the National Basic Research Project of Nonlinear ScienceNingbo Youngster Science Foundation.
文摘In parametrically excited Faraday experiment the non-propagating solitons-breathers, kinksand breather pairs-have been observed at the interface of two insoluble liquids with different densities.Phenomena observed at the interface are similar to those on the surface, except that the eigenfrequencies are remarkably red-shifted, and the wave forms are flatter and less stable due to the presence of the upper liquid. A nonlinear Schrodinger equation with damping and drive terms has been derived to explain the new observations. Both experiment and theory show that the free surface wave is a special case of the interface wave.
基金the Natural Science Foundation of Education Department of Henan Province of China under Grant No.2007110010the Science Foundation of Henan University of Science and Technology under Grant Nos.2006ZY-001 and 2006ZY-011
文摘With the aid of a class of nonlinear ordinary differential equation （ODE） and its various positive solutions, four types of exact solutions of the generalized derivative nonlinear Sehrodinger equation （GDNLSE） have been found out, which are the bell-type solitary wave solution, the algebraic solitary wave solution, the kink-type solitary wave solution and the sinusoidal traveling wave solution, provided that the coefficients of GDNLSE satisfy certain constraint conditions. For more general GDNLSE, the similar results are also given.
文摘In this paper, the modified extended tanh method is used to construct more general exact solutions of a （2＋1）-dimensional nonlinear SchrSdinger equation. With the aid of Maple and Matlab software, we obtain exact explicit kink wave solutions, peakon wave solutions, periodic wave solutions and their 3D images.
基金Supported by the National Natural Science Foundation of China under Grant No.11461022the Major Natural Science Foundation of Yunnan Province under Grant No.2014FA037
文摘The generalized nonlinear Schrdinger equation with parabolic law nonlinearity is studied by using the factorization technique and the method of dynamical systems.From a dynamic point of view,the existence of smooth solitary wave,kink and anti-kink wave is proved and the sufficient conditions to guarantee the existence of the above solutions in different regions of the parametric space are given.Also,all possible explicit exact parametric representations of the waves are presented.
