On dynamics of the system of two coupled nonlinear Schrödinger in

Abstract

In this paper, we give a new proof of the scattering and blow-up theory of the two coupled nonlinear Schrödinger system via establishing the corresponding interaction Morawetz estimate and scattering criterion. The method of this paper simplifies the proof in Xu, and the result of the paper improves the result in Xu. KEYWORDS blowup, coupled NLS system, Morawetz estimate, scattering MSC CLASSIFICATION 35L70; 35Q55

Sharp conditions for scattering and blow-up for a system of NLS arising in optical materials with χ3 nonlinear response

“…By exploiting the tools obtained in the previous parts of the paper, we are now able to prove the scattering for non-radial and radial solutions to (1.1) given in Theorem 1.1. See [29][30][31] for analogous results for NLS systems of quadratic type.…”

Sharp conditions for scattering and blow-up for a system of NLS arising in optical materials with $χ^3$ nonlinear response

“…By exploiting the tools obtained in the previous parts of the paper, we are now able to prove the scattering for non-radial and radial solutions to (1.1) given in Theorem 1.1. See [25,32,33] for analogous results for NLS systems of quadratic type.…”

Criteria for finite time blow up for a system of Klein–Gordon equations

“…Remark 1.4. For systems of Schrödinger equations, the scattering property below the ground state has already been considered in [22,13,21]. We emphasize here that in the first two works the authors adopted Kenig-Merle's concentration-compactness argument [11] while in the third one the authors used Dodson-Murphy's interactive Morawetz estimate [7].…”