Asymptotic properties of solutions to dispersive equation of Schrodinger type

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  • Asymptotic properties of solutions to dispersive equation of Schrödinger type

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We find the asymptotic behavior for large time of solutions to the dispersive equations of Schrödinger type <br>ut-$¥frac{i}{¥rho}$ |∂x|ρu = 0, (t,x) ∈ R × R,<br>where ρ ≥ 2. We obtain some estimates of solutions of linear problem and apply them to nonlinear problems with power nonlinearities of order p ≥ 3. The nonexistence of wave operator and existence of the modified wave operator for the critical nonlinearity i λ |u|2u are studied.

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