riemann-hilbert problem
An integral equation related to the exterior riemann-hilbert problem on region with corners
... the Riemann-Hilbert problem (briefly the RH problem) for smooth arbitrary simply connected region for general indices via boundary integral ...RH problem does not include regions with ...
10
A Riemann–Hilbert problem for uncoupled BPS structures
... Riemann–Hilbert problems are inverse problems in the theory of differential equations. They classically consist in seeking a piecewise holomorphic function on C ∗ with values in a Lie group, with prescribed ...
22
A quantized Riemann-Hilbert problem in Donaldson-Thomas theory
... quantum Riemann- Hilbert problem under the conditions (a)-(d) of Definition ...quantum Riemann-Hilbert problem can be obtained by superimposing solutions to the problem ...
34
Explicit Solutions of the Coupled mKdV Equation by the Dressing Method via Local Riemann Hilbert Problem
... We study the coupled mKdV equation by the dressing method via local Riemann- Hilbert problem. With the help of the Lax pairs, we obtain the matrix Riemann- Hilbert problem with ...
10
Solvability of some classes of singular integral equations of convolution type via Riemann–Hilbert problem
... a Riemann–Hilbert problem with discontinuous coefficients and nodes s = 0, ∞, and its method of solution may be made fully analogous to those in ...
19
Nystrom method for solving non-uniquely solvable interior Riemann-Hilbert problem on region with corners via integral equation
... Platter problem. Other applications of the RH problem are in fluid dynamics and gas dynamics (Nasser, 2007; ...RH problem arises in a mixed boundary value ...RH problem (Hass, ...
20
Riemann–Hilbert approach and N soliton solution for an eighth order nonlinear Schrödinger equation in an optical fiber
... is divided into five sections. In the second section, we recall the Lax pair associated with Equation (2) and convert it into a more convenient form. In the third section, we carry out the spectral analysis, from which a ...
14
Riemann–Hilbert problems with shift on the Lyapunov curve for null-solutions of iterated Beltrami equations
... Combining Riemann BVP for β -analytic functions with Haseman problem for polyan- alytic functions, it is a natural idea to discuss Riemann–Hilbert problem with shift on the general ...
34
Riemann-Hilbert problems from Donaldson-Thomas theory
... We should admit straight away that at present there many unanswered questions and unsolved technical problems with the theory. In particular, for general BPS structures we have no existence or uniquness results for ...
47
An integral equation method for solving exterior Neumann problems on smooth regions
... Neumann problem is reduced to equivalent Riemann-Hilbert problem by using Cauchy-Riemann ...the Riemann-Hilbert problem based on an earlier work by Nasser ...
18
Riemann-Hilbert problems for the resolved conifold
... The form h−, −i, which in the general context of [6] is the Euler form of the relevant category, vanishes in this case because curves on a threefold have zero intersection number. This has the consequence that the BPS ...
35
A Boundary integral equation for the Neumann problem in bounded multiply connected region
... Neumann problem to the Riemann-Hilbert problem in multiply connected region, and then derive an integral equation with the Neumann kernel related to the Riemann-Hilbert ...
17
Nonnegative Solutions for a Riemann Liouville Fractional Boundary Value Problem
... If x is a fixed point of operator , then x is a solution of Equation (6) (or (7)), and hence x is a solution of problem ( E )-( BC ). Therefore we will study the existence (and uniqueness) of the fixed points of ...
12
Lax Entropy Conditions for the One-Dimensional Riemann Problem
... We have shown analytically that the FTCS method is unstable and confirmed this with a numerical attempt. Clearly the Roe-averaging method does not capture the expansion fan, while the Lax-Friedrichs method does. However ...
47
The Riemann Problem for the Simplified Combustion Model in Magnetogasdynamics
... the Riemann solutions of (1), (2) with the initial data (3) under the modified entropy conditions in ...the Riemann solutions are similar with that of the conventional gas dynamic combustion model (4) in ...
8
Riemann boundary-value problem for doubly-periodic bianalytic functions
... In 1935, Natanzon first made use of doubly-periodic bianalytic function to deal with a problem on stresses deriving from a stretched plate. In 1957, Erwe also studied other classes of doubly-periodic polyanalytic ...
20
Multiple Solutions for the Riemann Problem in the Porous Shallow Water Equations
... the Riemann problem on the dry bed for the classic Shallow water Equations is unique, and consists of a rarefaction wave connecting the left state to the right dry ...the Riemann problem on ...
9
Hilbert series and applications to graded rings
... on Hilbert series that we ex- pect to be useful in various ...fractional Riemann-Roch formula of Fletcher and Reid to write out explicit formulas for the Hilbert series P (t) in a number of cases of ...
7
Higher Arf Functions and Topology of the Moduli Space of Higher Spin Riemann Surfaces
... The classical spin structures (theta characteristics) on compact Riemann surfaces play an important role in algebraic geometry since Riemann [Rie53]. Their modern interpretation and classification as ...
38
A fourth-order elliptic Riemann type problem in \(\mathbb{R}^{3}\)
... elliptic equation and construct the explicit expressions of higher-order kernel functions. Some integral representation formulas and properties of the null solution of the fourth-order elliptic equations in Clifford ...
19