Abstract
We study the global existence and large time asymptotic behavior of solutions to the initial-boundary value problem for the nonlinear nonlocal Schrödinger equation on a segment
(0.1)
where the pseudodifferential operator has the dissipation propery and the symbol of order . We prove that if the initial data are small, then there exists a unique solution of the initial-boundary value problem (0.1) Moreover there exists a function such that the solution has the following large time asymptotics
where .
Funding Statement
This work is partially supported by CONACYT and COSNET.
Acknowledgement
We are grateful to an unknown referee for many useful suggestions and comments.
Citation
Elena I. Kaikina. Pavel I. Naumkin. Isahi Sánchez-Suárez. "Nonlinear nonlocal Schrödinger type equations on a segment." SUT J. Math. 40 (1) 75 - 90, January 2004. https://doi.org/10.55937/sut/1100200011
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