Modal expansions and completeness relations for some time-dependent Schrödinger equations

Peter D. Miller; N. N. Akhmediev

doi:10.1016/S0167-2789(98)00147-X

Modal expansions and completeness relations for some time-dependent Schrödinger equations

Peter D. Miller^*, N. N. Akhmediev

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

With the use of a variant of the method of separation of variables, the initial value problem for the time-dependent linear Schrödinger equation is solved exactly for a large class of potential functions related to multisoliton interactions in the vector nonlinear Schrödinger equation. Completeness of states is proved for absolutely continuous initial data in L₁.

Original language	English
Pages (from-to)	513-524
Number of pages	12
Journal	Physica D: Nonlinear Phenomena
Volume	123
Issue number	1-4
DOIs	https://doi.org/10.1016/S0167-2789(98)00147-X
Publication status	Published - 1998

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10.1016/S0167-2789(98)00147-X

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@article{6126cb8cbf3c418bbd68964d30e9e117,

title = "Modal expansions and completeness relations for some time-dependent Schr{\"o}dinger equations",

abstract = "With the use of a variant of the method of separation of variables, the initial value problem for the time-dependent linear Schr{\"o}dinger equation is solved exactly for a large class of potential functions related to multisoliton interactions in the vector nonlinear Schr{\"o}dinger equation. Completeness of states is proved for absolutely continuous initial data in L1.",

keywords = "Completeness relations, Exact solvability, Time-dependent Schr{\"o}dinger equations",

author = "Miller, {Peter D.} and Akhmediev, {N. N.}",

year = "1998",

doi = "10.1016/S0167-2789(98)00147-X",

language = "English",

volume = "123",

pages = "513--524",

journal = "Physica D: Nonlinear Phenomena",

issn = "0167-2789",

publisher = "Elsevier B.V.",

number = "1-4",

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TY - JOUR

T1 - Modal expansions and completeness relations for some time-dependent Schrödinger equations

AU - Miller, Peter D.

AU - Akhmediev, N. N.

PY - 1998

Y1 - 1998

N2 - With the use of a variant of the method of separation of variables, the initial value problem for the time-dependent linear Schrödinger equation is solved exactly for a large class of potential functions related to multisoliton interactions in the vector nonlinear Schrödinger equation. Completeness of states is proved for absolutely continuous initial data in L1.

AB - With the use of a variant of the method of separation of variables, the initial value problem for the time-dependent linear Schrödinger equation is solved exactly for a large class of potential functions related to multisoliton interactions in the vector nonlinear Schrödinger equation. Completeness of states is proved for absolutely continuous initial data in L1.

KW - Completeness relations

KW - Exact solvability

KW - Time-dependent Schrödinger equations

UR - http://www.scopus.com/inward/record.url?scp=0000216497&partnerID=8YFLogxK

U2 - 10.1016/S0167-2789(98)00147-X

DO - 10.1016/S0167-2789(98)00147-X

M3 - Article

SN - 0167-2789

VL - 123

SP - 513

EP - 524

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

IS - 1-4

ER -

Modal expansions and completeness relations for some time-dependent Schrödinger equations

Abstract

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