In this paper, we discuss conditional stability of solitary-wave solutions in the sense of Liapunov for the generalized compound KdV equation and the generalized compound KdV-Burgers equations. Linear stability of the...In this paper, we discuss conditional stability of solitary-wave solutions in the sense of Liapunov for the generalized compound KdV equation and the generalized compound KdV-Burgers equations. Linear stability of the exact solitary-wave solutions is proved for the above two types of equations when the small disturbance of travelling wave form satisfies some special conditions.展开更多
The compound KdV-Burgers equation and combined KdV-mKdV equation are real physical models concerning many branches in physics.In this paper,applying the improved trigonometric function method to these equations,rich e...The compound KdV-Burgers equation and combined KdV-mKdV equation are real physical models concerning many branches in physics.In this paper,applying the improved trigonometric function method to these equations,rich explicit and exact travelling wave solutions,which contain solitary-wave solutions,periodic solutions,and combined formal solitary-wave solutions,are obtained.展开更多
The compound KdV-type equation with nonlinear terms of any order is reduced to the integral form. Using the complete discrimination system for polynomial, its all possible exact traveling wave solutions are obtained. ...The compound KdV-type equation with nonlinear terms of any order is reduced to the integral form. Using the complete discrimination system for polynomial, its all possible exact traveling wave solutions are obtained. Among those, a lot of solutions are new.展开更多
基金The project supported by National Natural Science Foundation of China under Grant No. 10371023 and Shanghai Leading Academic Discipline Project under Grant No. T0502）
文摘In this paper, we discuss conditional stability of solitary-wave solutions in the sense of Liapunov for the generalized compound KdV equation and the generalized compound KdV-Burgers equations. Linear stability of the exact solitary-wave solutions is proved for the above two types of equations when the small disturbance of travelling wave form satisfies some special conditions.
文摘The compound KdV-Burgers equation and combined KdV-mKdV equation are real physical models concerning many branches in physics.In this paper,applying the improved trigonometric function method to these equations,rich explicit and exact travelling wave solutions,which contain solitary-wave solutions,periodic solutions,and combined formal solitary-wave solutions,are obtained.
基金The project supported by Scientific Reseaxch Fund of Education Department of Heilongjiang Province of China under Grant No. 11511008
文摘The compound KdV-type equation with nonlinear terms of any order is reduced to the integral form. Using the complete discrimination system for polynomial, its all possible exact traveling wave solutions are obtained. Among those, a lot of solutions are new.
