JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (8): 50-54.doi: 10.6040/j.issn.1671-9352.0.2018.334

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Inverse spectral results for AKNS systems with partial information on the potentials

  

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xian 710119, Shaanxi, China
  • Online:2019-08-20 Published:2019-07-03

Abstract: We consider the AKNS systems on the interval[0,1] and prove that two potentials already known on [a,1](a∈(0,1/2])and their difference in Lp are equal if the number of their common eigenvalues is sufficiently large. The result here is to write down explicitly this number in terms of p(and a)showing the role of p.

Key words: AKNS symtem, potential function, inverse problem

CLC Number: 

  • O175.1
[1] AMOUR L. Inverse spectral theory for the AKNS system with separated boundary conditions[J]. Inverse Problems, 1993, 9:507-523.
[2] WATSON B A. Inverse spectral problems for weighted Dirac systems[J]. Inverse Problem, 1999, 15(3):793-80.
[3] GASYMOV M G, LEVITAN B M. Determining the Dirac system from scattering phase[J]. Dokl Akad Nauk SSSR, 1996, 167:1219-1222.
[4] LEVITAN B M, SARGSJAN I S. Sturm-Liouville and Dirac operators[M]. Berlin: Spriger, 1988.
[5] PÖSCHEL J, TUBOWITZ E. Inverse spectral theory academic press[M]. New York: AMS, 1987.
[6] DELRIO R, GRÉBERT B. Inverse spectral result for AKNS systems with partial information on the potentials[J]. Mathematical Physics, Analysis and Geometry, 2001, 4(3):229-244.
[7] MIKLÓS H. On the inverse spectral theory of Schrödinger and Dirac operators[J]. Amer Math Soc Transl, 2001, 353:4155-4171.
[8] AMOUR L, RAOUX T. Inverse spectral results for Schrödinger operators on the unit interval with potentials in Lp spaces[J]. Inverse Problems, 2007, 23:2367-2373.
[9] LENIN, B Js. Distribution of zeros of entire functions[M]. New York: AMS, 1964.
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