Abstract
The Shabat equation¶¶\( f'(z) + q^{2}f'(qz) + f^{2}(z) - q^{2}f^{2}(qz) = \mu \)¶ is the simplest self-similar reduction of the so called dressing chain for constructing and analysing exactly solvable Schrodinger equations. It is also useful to the study of the q-deformed Heisenberg-Weyl algebra. The objective of this paper is to investigate the existence of analytic solutions in the critical case where the complex parameter q is on the unit circle. The main result is that for any q belonging to a certain set of complex numbers on the unit circle with measure \( 2\pi \) the Shabat equation has a unique analytic solution in a neighborhood of the origin with any prescribed value at the origin.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
