The solvability and explicit solutions of singular integral–differential equations of non-normal type via Riemann–Hilbert problem

2020 ◽  
Vol 374 ◽  
pp. 112759
Author(s):  
Pingrun Li
Keyword(s):  
Differential Equations ◽  
Singular Integral ◽  
Hilbert Problem ◽  
Explicit Solutions ◽  
Normal Type ◽  
Integral Differential Equations ◽  
Riemann Hilbert Problem

scholarly journals Some explicit solutions to the Riemann–Hilbert problem

2009 ◽  
pp. 85-112 ◽  
Author(s):  
Philip Boalch
Keyword(s):  
Hilbert Problem ◽  
Explicit Solutions ◽  
Riemann Hilbert Problem

MONODROMY ARISING FROM THE MARKOFF THEORY

2006 ◽  
Vol 20 (11n13) ◽  
pp. 1819-1832
Author(s):  
SERGE PERRINE
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Free Group ◽  
Monodromy Group ◽  
Hilbert Problem ◽  
Monodromy Representation ◽  
Poincare Group ◽  
Complete Family ◽  
Computation Theory ◽  
Riemann Hilbert Problem

In a former work, recalling what the Markoff theory is, we summarized some existing links with the group GL(2, ℤ) of 2 × 2 matrices. We also quoted the relation with conformal punctured toruses. The monodromy representation of the Poincaré group of such a torus was considered. Here we explicit the corresponding solution of the associated Riemann-Hilbert problem, and the resulting Fuchs differential equation. We precisely describe how the calculus runs. The main result is the description of a complete family of Fuchs differential equations with, as the monodromy group, the free group with two generators. We also identify a link with some eigenvalues of a Laplacian. The introduction explains the links that we see with information and computation theory (classical or quantum).

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