Complex WKB method for difference equations in unbounded domains

2016 ◽  
Author(s):  
Alexander Fedotov ◽  
Ekaterina Shchetka
Keyword(s):  
Difference Equations ◽  
Unbounded Domains ◽  
Wkb Method ◽  
Complex Wkb Method

The Complex WKB Method for Difference Equations in Bounded Domains

2017 ◽  
Vol 224 (1) ◽  
pp. 157-169 ◽  
Author(s):  
A. A. Fedotov ◽  
E. V. Shchetka
Keyword(s):  
Difference Equations ◽  
Bounded Domains ◽  
Wkb Method ◽  
Complex Wkb Method

scholarly journals The Complex WKB Method for Difference Equations and Airy Functions

2019 ◽  
Vol 51 (6) ◽  
pp. 4413-4447 ◽  
Author(s):  
Alexander Fedotov ◽  
Frédéric Klopp
Keyword(s):  
Difference Equations ◽  
Wkb Method ◽  
Airy Functions ◽  
Complex Wkb Method

scholarly journals On the Complex WKB Method for a Secondary Turning Point Problem

2001 ◽  
Vol 24 (2) ◽  
pp. 343-358 ◽  
Author(s):  
Minoru NAKANO
Keyword(s):  
Turning Point ◽  
Point Problem ◽  
Wkb Method ◽  
Complex Wkb Method

The Complex WKB Method for Nonlinear Equations 1: Linear Theory (Victor P. Maslov)

SIAM Review ◽  
1996 ◽  
Vol 38 (1) ◽  
pp. 168-171
Author(s):  
Evans M. Harrell, II
Keyword(s):  
Linear Theory ◽  
Nonlinear Equations ◽  
Wkb Method ◽  
Complex Wkb Method

The Complex WKB Method for Nonlinear Equations I

1994 ◽  
Author(s):  
Victor P. Maslov
Keyword(s):  
Nonlinear Equations ◽  
Wkb Method ◽  
Complex Wkb Method

Using the complex WKB method for studying the evolution of initial pulses obeying the nonlinear Schr�dinger equation

1993 ◽  
Vol 36 (5) ◽  
pp. 431-437
Author(s):  
A. V. Shapovalov ◽  
S. N. Yurchenko
Keyword(s):  
Wkb Method ◽  
Dinger Equation ◽  
Complex Wkb Method

scholarly journals DIFFERENCE AND DIFFERENTIAL EQUATIONS FOR THE COLORED JONES FUNCTION

2008 ◽  
Vol 17 (04) ◽  
pp. 495-510 ◽  
Author(s):  
STAVROS GAROUFALIDIS
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Difference Equations ◽  
First Principles ◽  
Wkb Method ◽  
Laurent Polynomials ◽  
Linear Ordinary Differential Equations ◽  
Skein Module ◽  
Loop Expansion ◽  
Kauffman Bracket Skein Module

The colored Jones function of a knot is a sequence of Laurent polynomials. It was shown by Le and the author that such sequences are q-holonomic, that is, they satisfy linear q-difference equations with coefficients Laurent polynomials in q and qn. We show from first principles that q-holonomic sequences give rise to modules over a q-Weyl ring. Frohman–Gelca–LoFaro have identified the latter ring with the ring of even functions of the quantum torus, and with the Kauffman bracket skein module of the torus. Via this identification, we study relations among the orthogonal, peripheral and recursion ideal of the colored Jones function, introduced by the above mentioned authors. In the second part of the paper, we convert the linear q-difference equations of the colored Jones function in terms of a hierarchy of linear ordinary differential equations for its loop expansion. This conversion is a version of the WKB method, and may shed some information on the problem of asymptotics of the colored Jones function of a knot.

Sign in / Sign up

Export Citation Format

Share Document