On the direct scattering problem for the Wadati–Konno–Ichikawa equation with box‐like initial value. (31st March 2021)

• Record Type: Journal Article
• Authors: Tu, Youzhi; Xu, Jian
• Is Part Of: Mathematical methods in the applied sciences. Volume 44:Number 13(2021)
• Page Start: 10899
• Page End: 10904
• Publication Date: 2021-03-31
• Subjects: box initial value problem -- completely integrable system -- direct scattering data -- WKI equation; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.7321
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : We consider the direct scattering problem for a highly nonlinear complete integrable equation introduced by Wadati–Konno–Ichikawa (WKI), which describes nonlinear transverse oscillations of elastic beams under tension, with box‐like initial value. We show that in some cases of the initial value, the scattering data may have no zeros in upper half plane of the spectral variable. And furthermore in other cases, the scattering data may have infinitely many simple zeros, which seems not to be found before in the literature of the WKI equation.