In an Ocean or a River:Bilinear Auto-Backlund Transformations and Similarity Reductions on an Extended Time-Dependent(3+1)-Dimensional Shallow Water Wave Equation  

作　　者：GAO Xin-yi 

机构地区：[1]College of Science,and Beijing Key Laboratory on Integration and Analysis of Large-Scale Stream Data,North China University of Technology,Beijing 100144,China [2]Beijing Laboratory of New Energy Storage Technology,Beijing Municipal Education Commission,Beijing 102206,China

出　　处：《China Ocean Engineering》2025年第1期160-165,共6页中国海洋工程(英文版)

基　　金：financially supported by the Scientific Research Foundation of North China University of Technology(Grant Nos.11005136024XN147-87 and 110051360024XN151-86).

摘　　要：With respect to oceanic fluid dynamics,certain models have appeared,e.g.,an extended time-dependent(3+1)-dimensional shallow water wave equation in an ocean or a river,which we investigate in this paper.Using symbolic computation,we find out,on one hand,a set of bilinear auto-Backlund transformations,which could connect certain solutions of that equation with other solutions of that equation itself,and on the other hand,a set of similarity reductions,which could go from that equation to a known ordinary differential equation.The results in this paper depend on all the oceanic variable coefficients in that equation.

关 键 词：OCEAN RIVER extended time-dependent(3+1)-dimensional shallow water wave equation bilinear auto-Bäcklund transformation similarity reduction symbolic computation 

分 类 号：O17[理学—数学]