THE GLM REPRESENTATION OF THE TWO-COMPONENT NONLINEAR SCHRÖDINGER EQUATION ON THE HALF-LINE

Acta mathematica scientia,Series B ›› 2018, Vol. 38 ›› Issue (6): 1846-1860.

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THE GLM REPRESENTATION OF THE TWO-COMPONENT NONLINEAR SCHRÖDINGER EQUATION ON THE HALF-LINE

Qiaozhen ZHU¹, Engui FAN¹, Jian XU²

1 School of Mathematical Sciences, Fudan University, Shanghai 200433, China;
2 College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China

Received:2017-07-20 Revised:2018-02-28 Online:2018-12-25 Published:2018-12-28
Contact: Engui FAN E-mail:faneg@fudan.edu.cn
Supported by:
This work was support by NSFC (11671095; 11501365). Shanghai Sailing Program supported by Science and Technology Commission of Shanghai Municipality under Grant NO.15YF1408100, Shanghai Youth Teacher Assistance program NO.ZZslg15056 and the Hujiang Foundation of China (B14005).

Abstract

Abstract: The Gelfand-Levitan-Marchenko representation is used to analyze the initial-boundary value problem of two-component nonlinear Schrödinger equation on the half-line. It has shown that the global relation can be effectively analyzed by the Gelfand-Levitan-Marchenko representation. we also derive expressions for the Dirichlet-to-Neumann map to characterize the unknown boundary values.

Key words: Gelfand-Levitan-Marchenko representation, initial-boundary value problem, two-component nonlinear Schrödinger equation

Qiaozhen ZHU, Engui FAN, Jian XU. THE GLM REPRESENTATION OF THE TWO-COMPONENT NONLINEAR SCHRÖDINGER EQUATION ON THE HALF-LINE[J].Acta mathematica scientia,Series B, 2018, 38(6): 1846-1860.

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References

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THE GLM REPRESENTATION OF THE TWO-COMPONENT NONLINEAR SCHRÖDINGER EQUATION ON THE HALF-LINE

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