简介:利用推广形式的二重复Ernst方程的已知种子解,通过一种Bācklund变换来获得新解,从稳态轴对称引力真空场的二重复Ernst方程出发,通过定义新坐标x1=P+JZ,x2=P-J2得到一种推广形式的二重复Ernst方程,并通过对其种子解进行Ⅰ变换。从而得到一种新形式的Bcklund变换来生成Ernst方程的新解,此Ⅰ变换满足群性质.
简介:Underinvestigationinthispaperisa(3+1)-dimensionalvariable-coefficientKadomtsev–Petviashviliequation,whichdescribesthepropagationofsurfaceandinternalwaterwaves.ByvirtueofthebinaryBellpolynomials,symboliccomputationandauxiliaryindependentvariable,thebilinearforms,solitonsolutions,B¨acklundtransformationsandLaxpairareobtained.Variablecoefficientsoftheequationcanaffectthesolitonicstructure,whentheyarespeciallychosen,whilecurvedandlinearsolitonsareillustrated.Elasticcollisionsbetween/amongtwoandthreesolitonsarediscussed,throughwhichthesolitonskeeptheiroriginalshapesinvariantexceptforsomephaseshifts.