Frontiers of Mathematics in China >

2019 , Vol. 14 >Issue 5: 1063 - 1075

DOI: https://doi.org/10.1007/s11464-019-0795-3

RESEARCH ARTICLE

Spectral analysis of generalized Volterra equation

  • Junyi ZHU 1 ,
  • Xinxin MA 1 ,
  • Zhijun QIAO , 2
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  • 1. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China
  • 2. School of Mathematical and Statistical Sciences, University of Texas Rio Grande Valley, Edinburg, TX 78539, USA

Received date: 08 May 2019

Accepted date: 02 Oct 2019

Published date: 15 Oct 2019

Copyright

2019 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature
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Abstract

A generalized Volterra lattice with a nonzero boundary condition is considered by virtue of the inverse scattering transform. The two-sheeted Riemann surface associated with the boundary problem is transformed into the Riemann sphere by introducing a suitable variable transformation. The associated spectral properties of the lattice in single-valued variable was discussed. The constraint condition about the nonzero boundary condition and the scattering data is found.

Key words： Volterra lattice; nonzero boundary condition; inverse scattering transform

Cite this article

Junyi ZHU , Xinxin MA , Zhijun QIAO . Spectral analysis of generalized Volterra equation[J]. Frontiers of Mathematics in China, 2019 , 14(5) : 1063 -1075 . DOI: 10.1007/s11464-019-0795-3

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