The conservation laws for the （1＋2）-dimensional Zakharov-Kuznetsov modified equal width （ZK-MEW） equation with power law nonlinearity are constructed by using Noether＇s approach through an interesting method of ...The conservation laws for the （1＋2）-dimensional Zakharov-Kuznetsov modified equal width （ZK-MEW） equation with power law nonlinearity are constructed by using Noether＇s approach through an interesting method of increasing the order of this equation. With the aid of an obtained conservation law, the generalized double reduction theorem is applied to this equation. It can be shown that the reduced equation is a second order nonlinear ODE. FinaJ1y, some exact solutions for a particular case of this equation are obtained after solving the reduced equation.展开更多
The general bright-dark mixed N-soliton solution of the two-dimensional Maccari system is obtained with the KP hierarchy reduction method. The dynamics of single and two solitons are discussed in detail. Asymptotic an...The general bright-dark mixed N-soliton solution of the two-dimensional Maccari system is obtained with the KP hierarchy reduction method. The dynamics of single and two solitons are discussed in detail. Asymptotic analysis shows that two solitons undergo elastic collision accompanied by a position shift. Furthermore, our analysis on mixed soliton bound states shows that arbitrary higher-order soliton bound states can take place.展开更多
To find intrinsically different symmetry reductions and inequivalent group invariant solutions of the 2D unsteady incompressible boundary-layer equations, a two-dimensional optimal system is constructed which attribut...To find intrinsically different symmetry reductions and inequivalent group invariant solutions of the 2D unsteady incompressible boundary-layer equations, a two-dimensional optimal system is constructed which attributed to the classification of the corresponding Lie subalgebras. The comprehensiveness and inequivalence of the optimal system are shown clearly under different values of invariants. Then by virtue of the optimal system obtained, the boundary-layer equations are directly reduced to a system of ordinary differential equations(ODEs) by only one step. It has been shown that not only do we recover many of the known results but also find some new reductions and explicit solutions, which may be previously unknown.展开更多
To construct the one-dimensional optimal system of finite dimensional Lie algebra automatically,we develop a new Maple package One Optimal System.Meanwhile,we propose a new method to calculate the adjoint transformati...To construct the one-dimensional optimal system of finite dimensional Lie algebra automatically,we develop a new Maple package One Optimal System.Meanwhile,we propose a new method to calculate the adjoint transformation matrix and find all the invariants of Lie algebra in spite of Killing form checking possible constraints of each classification.Besides,a new conception called invariance set is raised.Moreover,this Maple package is proved to be more efficiency and precise than before by applying it to some classic examples.展开更多
基金Supported by the Fundamental Research Funds for the Central Universities under Grant No.2013XK03the National Natural Science Foundation of China under Grant No.11371361
文摘The conservation laws for the （1＋2）-dimensional Zakharov-Kuznetsov modified equal width （ZK-MEW） equation with power law nonlinearity are constructed by using Noether＇s approach through an interesting method of increasing the order of this equation. With the aid of an obtained conservation law, the generalized double reduction theorem is applied to this equation. It can be shown that the reduced equation is a second order nonlinear ODE. FinaJ1y, some exact solutions for a particular case of this equation are obtained after solving the reduced equation.
基金Supported by the Global Change Research Program of China under Grant No 2015CB953904the National Natural Science Foundation of China under Grant Nos 11675054 and 11435005the Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things under Grant No ZF1213
文摘The general bright-dark mixed N-soliton solution of the two-dimensional Maccari system is obtained with the KP hierarchy reduction method. The dynamics of single and two solitons are discussed in detail. Asymptotic analysis shows that two solitons undergo elastic collision accompanied by a position shift. Furthermore, our analysis on mixed soliton bound states shows that arbitrary higher-order soliton bound states can take place.
基金Supported by the Global Change Research Program of China under Grant No.2015CB953904National Natural Science Foundation of China under Grant Nos.11275072,11435005,11675054Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things under Grant No.ZF1213
文摘To find intrinsically different symmetry reductions and inequivalent group invariant solutions of the 2D unsteady incompressible boundary-layer equations, a two-dimensional optimal system is constructed which attributed to the classification of the corresponding Lie subalgebras. The comprehensiveness and inequivalence of the optimal system are shown clearly under different values of invariants. Then by virtue of the optimal system obtained, the boundary-layer equations are directly reduced to a system of ordinary differential equations(ODEs) by only one step. It has been shown that not only do we recover many of the known results but also find some new reductions and explicit solutions, which may be previously unknown.
基金Supported by the Global Change Research Program of China under Grant No.2015CB95390National Natural Science Foundation of China under Grant Nos.11675054 and 11435005Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things under Grant No.ZF1213
文摘To construct the one-dimensional optimal system of finite dimensional Lie algebra automatically,we develop a new Maple package One Optimal System.Meanwhile,we propose a new method to calculate the adjoint transformation matrix and find all the invariants of Lie algebra in spite of Killing form checking possible constraints of each classification.Besides,a new conception called invariance set is raised.Moreover,this Maple package is proved to be more efficiency and precise than before by applying it to some classic examples.
