Results 21 to 30 of about 39,546 (135)

Response of a Fermi gas to time-dependent perturbations: Riemann-Hilbert approach at non-zero temperatures

, 2006
We provide an exact finite temperature extension to the recently developed Riemann-Hilbert approach for the calculation of response functions in nonadiabatically perturbed (multi-channel) Fermi gases.
Bernd Braunecker, F. G. Fumi, G. D. Mahan, N. I. Muskhelishvili, N. P. Vekua, R. Estrada   +5 more
core   +1 more source

Rational Solutions of the Painlev\'e-II Equation Revisited [PDF]

, 2017
The rational solutions of the Painlev\'e-II equation appear in several applications and are known to have many remarkable algebraic and analytic properties. They also have several different representations, useful in different ways for establishing these
Miller, Peter D., Sheng, Yue
core   +3 more sources

A Riemann–Hilbert approach to solution of the modified focusing complex short pulse equation

Frontiers in Applied Mathematics and Statistics
We develop a Riemann–Hilbert approach to the modified focusing complex short pulse (mfcSP) equationuxt=u+12u¯(u2)xxwith zero boundary conditions (as |x| → ∞).
Ruslan Barkov, Dmitry Shepelsky, Dmitry Shepelsky   +2 more
doaj   +1 more source

Exact solutions of a local fractional nonisospectral complex mKdV equation based on Riemann–Hilbert method with time-varying spectrum

Alexandria Engineering Journal
This article combines the Riemann–Hilbert method with fractional power-law time-varying spectrum for the first time to solve a time fractional nonisospectral complex mKdV (tfniscmKdV) equation. Firstly, the tfniscmKdV equation and its associated Lax pair
Bo Xu, Sheng Zhang
doaj   +1 more source

Invariant Measure and Universality of the 2D Yang–Mills Langevin Dynamic

Communications on Pure and Applied Mathematics, EarlyView.
ABSTRACT We prove that the Yang–Mills (YM) measure for the trivial principal bundle over the two‐dimensional torus, with any connected, compact structure group, is invariant for the associated renormalised Langevin dynamic. Our argument relies on a combination of regularity structures, lattice gauge‐fixing and Bourgain's method for invariant measures ...
Ilya Chevyrev, Hao Shen
wiley   +1 more source

Dispersionless Hierarchies, Hamilton-Jacobi Theory and Twistor Correspondences

, 1997
The dispersionless KP and Toda hierarchies possess an underlying twistorial structure. A twistorial approach is partly implemented by the method of Riemann-Hilbert problem. This is however still short of clarifying geometric ingredients of twistor theory,
Boyer, Carroll, Dubrovin, Dubrovin, Gibbons, Gibbons, Gindikin, Hitchin, Hitchin, Jones, Kanehisa Takasaki, Kodama, Kodama, Kodama, Krichever, Krichever, Lebedev, Orlov, Partha Guha, Penrose, Takasaki, Takasaki, Takasaki, Takasaki, Takasaki, Takasaki, Takasaki, Takasaki, Tsarev, Ward, Zakharov   +30 more
core   +2 more sources

The Benjamin–Ono Equation in the Zero‐Dispersion Limit for Rational Initial Data: Generation of Dispersive Shock Waves

Communications on Pure and Applied Mathematics, EarlyView.
ABSTRACT The leading‐order asymptotic behavior of the solution of the Cauchy initial‐value problem for the Benjamin–Ono equation in L2(R)$L^2(\mathbb {R})$ is obtained explicitly for generic rational initial data u0$u_0$. An explicit asymptotic wave profile uZD(t,x;ε)$u^\mathrm{ZD}(t,x;\epsilon)$ is given, in terms of the branches of the multivalued ...
Elliot Blackstone, Louise Gassot, Patrick Gérard, Peter D. Miller   +3 more
wiley   +1 more source

Universality for eigenvalue correlations at the origin of the spectrum

, 2003
We establish universality of local eigenvalue correlations in unitary random matrix ensembles (1/Z_n) |\det M|^{2\alpha} e^{-n\tr V(M)} dM near the origin of the spectrum.
Kuijlaars, A. B. J., Vanlessen, M.
core   +3 more sources

A highly accurate numerical method for solving boundary value problem of generalized Bagley‐Torvik equation

Mathematical Methods in the Applied Sciences, EarlyView.
A highly accurate numerical method is given for the solution of boundary value problem of generalized Bagley‐Torvik (BgT) equation with Caputo derivative of order 0<β<2$$ 0<\beta <2 $$ by using the collocation‐shooting method (C‐SM). The collocation solution is constructed in the space Sm+1(1)$$ {S}_{m+1}^{(1)} $$ as piecewise polynomials of degree at ...
Suzan Cival Buranay, Mtema James Chin, Nazim I. Mahmudov   +2 more
wiley   +1 more source

Numerical solution of Riemann-Hilbert problems: Painleve II [PDF]

, 2009
We describe a new spectral method for solving matrix-valued Riemann-Hilbert problems numerically. We demonstrate the effectiveness of this approach by computing solutions to the homogeneous Painleve II equation.
Olver, Sheehan
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