文献类型：期刊文献

中文题名：Modified(1+1)-Dimensional Displacement Shallow Water Wave System

英文题名：Modified (1+1)-Dimensional Displacement Shallow Water Wave System

作者：Liu Ping[1];Yang Jian-Jun[1];Ren Bo[2]

机构：[1]Univ Elect Sci & Technol China, Zhongshan Inst, Coll Elect & Informat Engn, Zhongshan 528402, Peoples R China;[2]Shaoxing Univ, Inst Nonlinear Sci, Shaoxing 312000, Peoples R China

年份：2013

卷号：30

期号：10

中文期刊名：中国物理快报：英文版

外文期刊名：CHINESE PHYSICS LETTERS

收录：SCI-EXPANDED(收录号：WOS:000326492900001)、CSTPCD、、EI(收录号：20220711659879)、Scopus(收录号：2-s2.0-84887070999)、WOS、CSCD、CSCD2013_2014

基金：Supported by the National Natural Science Foundation of China (Nos 11305031 and 11305106), the Natural Science Foundation of Guangdong Province (No S2013010011546), the Natural Science Foundation of Zhejiang Province (No LQ13A050001), and Science and Technology Project Foundation of Zhongshan (No 20123A326).

语种：英文

中文关键词：equation;viscosity;system;

外文关键词：Water waves - Viscosity

中文摘要：Recently,a(1+1)-dimensional displacement shallow water wave system(1DDSWWS)was constructed by applying variational principle of the analytic mechanics under the Lagrange coordinates.However,fluid viscidity is not considered in the 1DDSWWS,which is the same as the famous Korteweg-de Vries(KdV)equation.We modify the 1DDSWWS and add the term related to fluid viscosity to the model by means of dimension analysis.For the perfect fluids,the coefficient of kinematic viscosity is zero,then the modified 1DDSWWS(M1DDSWWS)will degenerate to 1DDSWWS.The KdV-Burgers equation and the Abel equation can be derived from the M1DDSWWS.The calculation on symmetry shows that the system is invariant under the Galilean transformations and the spacetime translations.Two types of exact solutions and some evolution graphs of the M1DDSWWS are proposed.

外文摘要：Recently, a (1+1)-dimensional displacement shallow water wave system (1DDSWWS) was constructed by applying variational principle of the analytic mechanics under the Lagrange coordinates. However, fluid viscidity is not considered in the 1DDSWWS, which is the same as the famous Korteweg-de Vries (KdV) equation. We modify the 1DDSWWS and add the term related to fluid viscosity to the model by means of dimension analysis. For the perfect fluids, the coefficient of kinematic viscosity is zero, then the modified 1DDSWWS (M1DDSWWS) will degenerate to 1DDSWWS. The KdV-Burgers equation and the Abel equation can be derived from the M1DDSWWS. The calculation on symmetry shows that the system is invariant under the Galilean transformations and the spacetime translations. Two types of exact solutions and some evolution graphs of the M1DDSWWS are proposed.