Modified Scattering States for Subcritical Derivative Nonlinear Schrödinger Equations

Abstract

We consider thre derivative nonlinear Schrödinger equations

where the coefficient a(t) satisfies the condition is a sufficiently small constant and We suppose that the initial data satisfy the exponential decay conditions. Then in the case we show that the usual scattering states exist, and in the other case we construct the modified scattering states.

Keywords:

• Nonlinear Schrödinger equations
• Asymptotic expansions
• Modified scattering states
• Subcritical nonlinearities

AMS Classification:

• 35A05
• 76B40
• 35Q35

^*Corresponding author. [email protected]—u.ac.jp

^† [email protected]

^‡ [email protected]

^*Corresponding author. [email protected]—u.ac.jp

^† [email protected]

^‡ [email protected]

Notes

^*Corresponding author. [email protected]—u.ac.jp

^† [email protected]

^‡ [email protected]