Abstract
We study the existence and scattering of global small amplitude solutions to modified improved Boussinesq equations in one dimension with nonlinear term behaving as a power as . Solutions are considered in space for all . According to the value of s , the power nonlinearity exponent p is determined. Liu (Liu 1996 Indiana Univ. Math. J . 45 , 797–816) obtained the minimum value of p greater than 8 at for sufficiently small Cauchy data. In this paper, we prove that p can be reduced to be greater than at and the corresponding solution u has the time decay, such as as . We also prove non-existence of non-trivial asymptotically free solutions for under vanishing condition near zero frequency on asymptotic states.
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