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In this paper,we will consider the existence and the uniqueness of the global solution for the Cauchy problem of the generalized Benney-Luke equation utt-△utt +△2u-m△u + α (2▽u · ▽ut + ut△u) + β▽· (|▽u|p▽u) =O,(1)u(x,0) =(ψ)(x),ut(x,0) =ψ(x),(2)where u(x,t) denotes an unknown function of variables x =(x1,x2,.…,xn) ∈ Rn(n =1,2,3,4) and t ∈ R+,A is Laplaces operator,▽ is the Hamiltons operator,m > 0,β and α are constants,p > 0 is constant with 0
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