11,061 research outputs found
New integrable systems of derivative nonlinear Schr\"{o}dinger equations with multiple components
The Lax pair for a derivative nonlinear Schr\"{o}dinger equation proposed by
Chen-Lee-Liu is generalized into matrix form. This gives new types of
integrable coupled derivative nonlinear Schr\"{o}dinger equations. By virtue of
a gauge transformation, a new multi-component extension of a derivative
nonlinear Schr\"{o}dinger equation proposed by Kaup-Newell is also obtained.Comment: 15 pages, LaTeX209, to appear in Phys. Lett.
Comment on "Discretisations of constrained KP hierarchies"
In the recent paper (R. Willox and M. Hattori, arXiv:1406.5828), an
integrable discretization of the nonlinear Schr\"odinger (NLS) equation is
studied, which, they think, was discovered by Date, Jimbo and Miwa in 1983 and
has been completely forgotten over the years. In fact, this discrete NLS
hierarchy can be directly obtained from an elementary auto-B\"acklund
transformation for the continuous NLS hierarchy and has been known since 1982.
Nevertheless, it has been rediscovered again and again in the literature
without attribution, so we consider it meaningful to mention overlooked
original references on this discrete NLS hierarchy.Comment: 6 pages; references adde
- …