Refine search
Actions for selected content:
1 results
Nonstationary Schrödinger equation with rational potentials
-
- Journal:
- Journal of Nonlinear Waves / Volume 2 / 2026
- Published online by Cambridge University Press:
- 12 August 2026, e19
-
- Article
-
- You have access
- Open access
- HTML
- Export citation
-
The nonstationary Schrödinger equation (NSE) with a special class of rational potentials is investigated via binary Darboux transformation. It is shown that in this case, the NSE corresponds to the focusing nonlinear Schrödinger equation (NLS):
$ir_y=r_{xx}+|r|^2r$ where 
$r(x,y)$ is rational with non-vanishing boundary conditions: 
$|r| \to b$ as 
$|x| \to \infty$. These rational solutions of NLS are the so-called rogue wave solutions that have been studied extensively for the last 15 years or so. Furthermore, these rational potentials of the NSE are also shown to correspond to a special family of rational, multi-lump solutions of the Kadomtsev–Petviasvili I equation with multiple peaks in the 
$xy$-plane and vanishing as 
$x^2+y^2 \to \infty$.
