The extended symmetry approach is used to study the general Korteweg-de Vries-type （KdV-type） equation. Several variable-coefficient equations are obtained. The solutions of these resulting equations can be construc...The extended symmetry approach is used to study the general Korteweg-de Vries-type （KdV-type） equation. Several variable-coefficient equations are obtained. The solutions of these resulting equations can be constructed by the solutions of original models if their solutions are well known, such as the standard constant coefficient KdV equation and the standard compound KdV--Burgers equation, and so on. Then any one of these variable-coefficient equations can be considered as an original model to obtain new variable-coefficient equations whose solutions can also be known by means of transformation relations between solutions of the resulting new variable-coefficient equations and the original equation.展开更多
The Korteweg-de Vries(Kd V)-type equations have been seen in fluid mechanics,plasma physics and lattice dynamics,etc. This paper will address the bilinearization problem for some higher-order Kd V equations. Based on ...The Korteweg-de Vries(Kd V)-type equations have been seen in fluid mechanics,plasma physics and lattice dynamics,etc. This paper will address the bilinearization problem for some higher-order Kd V equations. Based on the relationship between the bilinear method and Bell-polynomial scheme,with introducing an auxiliary independent variable,we will present the general bilinear forms. By virtue of the symbolic computation,one-and two-soliton solutions are derived.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No. 10675065)the Scientific Research Fundof the Education Department of Zhejiang Province of China (Grant No. 20070979)
文摘The extended symmetry approach is used to study the general Korteweg-de Vries-type （KdV-type） equation. Several variable-coefficient equations are obtained. The solutions of these resulting equations can be constructed by the solutions of original models if their solutions are well known, such as the standard constant coefficient KdV equation and the standard compound KdV--Burgers equation, and so on. Then any one of these variable-coefficient equations can be considered as an original model to obtain new variable-coefficient equations whose solutions can also be known by means of transformation relations between solutions of the resulting new variable-coefficient equations and the original equation.
基金Supported by the National Natural Science Foundation of China under Grant No.11272023the Open Fund of State Key Laboratory of Information Photonics and Optical Communications(Beijing University of Posts and Telecommunications)by the Fundamental Research Funds for the Central Universities of China under Grant No.2011BUPTYB02
文摘The Korteweg-de Vries(Kd V)-type equations have been seen in fluid mechanics,plasma physics and lattice dynamics,etc. This paper will address the bilinearization problem for some higher-order Kd V equations. Based on the relationship between the bilinear method and Bell-polynomial scheme,with introducing an auxiliary independent variable,we will present the general bilinear forms. By virtue of the symbolic computation,one-and two-soliton solutions are derived.
