9 research outputs found
Asymptotic behavior for the long-range nonlinear Schr\"odinger equation on star graph with the Kirchhoff boundary condition
Full text linkWe consider the cubic nonlinear Schr\"{o}dinger equation on the star graph
with the Kirchhoff boundary condition. We prove modified scattering for the
final state problem and the initial value problem. Moreover, we also consider
the failure of scattering for the Schr\"{o}dinger equation with power-type
long-range nonlinearities. These results are extension of the results for NLS
on the one dimensional Euclidean space
Asymptotic behavior of solutions to a quadratic nonlinear Schrodinger system with mass resonance (Harmonic Analysis and Nonlinear Partial Differential Equations)
Get PDFAsymptotic behavior and critical regularity of solutions to systems of nonlinear Schrödinger equations with mass resonance
No full textAsymptotic behavior of solutions to a quadratic nonlinear Schrodinger system with mass resonance (Harmonic Analysis and Nonlinear Partial Differential Equations)
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