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We prove a weak form of the soliton resolution conjecture of boundedsolutions of high-dimensional fourth-order Schrodinger equations. The resultrelies upon two properties to be proved: the asymptotic frequency localizationand the asymptotic spatial localization. In order to prove the asymptoticfrequency localization we use the fact that the high frequency pieces of thefree solution have better dispersive properties than the lower ones. In orderto prove the asymptotic spatial localization, we use the symmetries of thephase of the fundamental solution.

A weak form of the soliton resolution conjecture for high-dimensional fourth-order Schrodinger equations