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- W2023359295 abstract "We consider a spatially uniform asymptotic representation at large times of the solution to the Cauchy problem for the non-linear Schrodinger equation. If the non-linear term decreases in time faster than the linear terms, then the asymptotics are quasi-linear. Of particular interest is the case in which the non-linearity decreases in time at the same rate as or even more slowly then the linear terms and thus has a stronger effect on the solution asymptotics at large times. In this paper we employ an appropriate change of variables to reduce this case to the quasi-linear one. Namely, we derive an integral equation with rapidly decreasing non-linearity for the new unknown function, which can be solved by the method of successive approximations. Thus, we have a constuctive algorithm for calculating the asymptotics of the solution to the Cauchy problem for the non-linear Schrodinger equation from the initial data." @default.
- W2023359295 created "2016-06-24" @default.
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- W2023359295 date "1997-08-31" @default.
- W2023359295 modified "2023-10-16" @default.
- W2023359295 title "Solution asymptotics at large times for the non-linear Schrödinger equation" @default.
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- W2023359295 doi "https://doi.org/10.1070/im1997v061n04abeh000137" @default.
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