In this paper, generalized KdV equations are investigated by using a mathematical technique based on the reduction of order for solving differential equations. The compactons, solitons, solitary patterns and periodic ...In this paper, generalized KdV equations are investigated by using a mathematical technique based on the reduction of order for solving differential equations. The compactons, solitons, solitary patterns and periodic solutions for the equations presented in this paper are obtained. For these generalized KdV equations, it is found that the change of the exponents of the wave function u and the coefficient a, positive or negative, leads to the different physical structures of the solutions.展开更多
In this paper, the bifurcation method of dynamical systems and numerical approach of differential equations are employed to study CH-γ equation. Two new types of bounded waves are found. One of them is called the com...In this paper, the bifurcation method of dynamical systems and numerical approach of differential equations are employed to study CH-γ equation. Two new types of bounded waves are found. One of them is called the compacton. The other is called the generalized kink wave. Their planar graphs are simulated and their implicit expressions are given. The identity of theoretical derivation and numerical simulation is displayed.展开更多
文摘In this paper, generalized KdV equations are investigated by using a mathematical technique based on the reduction of order for solving differential equations. The compactons, solitons, solitary patterns and periodic solutions for the equations presented in this paper are obtained. For these generalized KdV equations, it is found that the change of the exponents of the wave function u and the coefficient a, positive or negative, leads to the different physical structures of the solutions.
基金supported by the National Natural Science Foundation of China(Grant No.10261008).
文摘In this paper, the bifurcation method of dynamical systems and numerical approach of differential equations are employed to study CH-γ equation. Two new types of bounded waves are found. One of them is called the compacton. The other is called the generalized kink wave. Their planar graphs are simulated and their implicit expressions are given. The identity of theoretical derivation and numerical simulation is displayed.
