Abstract
The main purpose of this paper is to consider the initial-boundary value problem for the 1D mixed nonlinear Schrödinger equation ut = iαuxx + βu2ūx + γ∣u∣2ux + i∣u∣2u on the half-line with inhomogeneous boundary condition. We combine Laplace transform method with restricted norm method to prove the local well-posedness and continuous dependence on initial and boundary data in low regularity Sobolev spaces. Moreover, we show that the nonlinear part of the solution on the half-line is smoother than the initial data.
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Guo, B., Wu, J. Local regularity properties for 1D mixed nonlinear Schrödinger equations on half-line. Front. Math. China 15, 1121–1142 (2020). https://doi.org/10.1007/s11464-020-0878-1
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DOI: https://doi.org/10.1007/s11464-020-0878-1
Keywords
- Mixed nonlinear Schrödinger (MNLS) equations
- initial-boundary value problem (IBVP)
- Bourgain spaces
- local well-posedness