简介:Theusual(1+1)-dimensionalSchwartzBoussinesqequationisextendedtothe(1+1)-dimensionalspace-timesym-metricformandthegeneral(n+1)-dimensionalspace-timesymmetricform.TheseextensionsarePainlevintegrableinthesensethattheypossessthePainlevproperty.Thesinglesolitonsolutionsandtheperiodictravellingwavesolutionsforarbitrarydimensionalspace-timesymmetricformareobtainedbythePainlev-Bcklundtransformation.