Inthispaper,weconsiderFPUlatticeswithparticlesofunitmass.Thedynamicsofthesystemisdescribedbytheinfinitesystemofsecondorderdifferentialequationsqn=U′(qn+1-qn)-U′(qn-qn-1),n∈Z,whereqndenotesthedisplacementofthen-thlatticesiteandUisthepotentialofinteractionbetweentwoadjacentparticles.InspiredbypreviousworkduetoSzulkinandWeth（Groundstatesolutionsforsomeindefinitevariationalproblems,J.Funct.Anal.,257（2009）,3802-3822）,weinvestigatetheexistenceofsolitarygroundwaves,i.e.,nontrivialsolutionswithleastpossibleenergy.
