Scattering for the 2d NLS with inhomogeneous nonlinearities

2025/12/12 by Baker, Luke
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Nonlinear Waves and Solitons #Nonlinear Partial Differential Equations

paper · doi:10.48550/arxiv.2512.11205

Abstract

We prove large-data scattering in H¹ for inhomogeneous nonlinear Schrödinger equations in two space dimensions for all powers p>0. We assume the inhomogeneity is nonnegative and repulsive; we additionally require decay at infinity in the case 0

Citations

• Scattering for the 1d NLS with inhomogeneous nonlinearities
• Well-posedness and scattering of odd solutions for the defocusing INLS in one dimension
• Scattering for the nonlinear Schrödinger equation with concentrated nonlinearity
• Decay of solutions to one-dimensional inhomogeneous nonlinear Schrödinger equations
• H¹ scattering for mass-subcritical NLS with short-range nonlinearity and initial data in Σ
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• Global well-posedness and scattering for the defocusing,\n L²-critical, nonlinear Schr "odinger equation when d = 1
• Global well-posedness and scattering for the defocusing, L²-critical, nonlinear Schrödinger equation when d ≥ 3
• Bilinear virial identities and applications
• The defocusing energy-critical nonlinear Schrödinger equation in higher dimensions
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Related

• Scattering for the 1d NLS with inhomogeneous nonlinearities
• Scattering theory in a weighted L² space for a class of the defocusing inhomogeneous nonlinear Schrödinger equation
• Scattering in the weighted L²-space for a 2D nonlinear Schrödinger equation with inhomogeneous exponential nonlinearity
• Energy scattering for a class of inhomogeneous nonlinear Schr "odinger\n equation in two dimensions
• Energy Scattering for Schrödinger Equation with Exponential Nonlinearity in Two Dimensions