The extended symmetry approach for studying the general Korteweg-de Vries-type equation  

作　　者：李志芳 阮航宇 

机构地区：[1]Department of Physics,Ningbo University

出　　处：《Chinese Physics B》2010年第4期3-10,共8页中国物理B（英文版）

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)

摘　　要：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.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.

关 键 词：extended symmetry approach general Korteweg-de Vries-type （KdV-type） equation variable-coefficient equation 

分 类 号：O411.1[理学—理论物理] O175[理学—物理]