Results 21 to 30 of about 303 (64)

Thomae type formulae for singular Z_N curves

, 2006
We give an elementary and rigorous proof of the Thomae type formula for singular $Z_N$ curves. To derive the Thomae formula we use the traditional variational method which goes back to Riemann, Thomae and Fuchs.Comment: 22 ...
A. Kitaev, A. Kokotov, A. Nakayashiki, A.N. Tjurin, A.R. Its, B.A. Dubrovin, D. Korotkin, D. Mumford, E.I. Zverovich, F. Klein, F. Klein, F.A. Smirnov, G.G. Diez, H. Burkhardt, H.E. Rauch, H.F. Baker, H.F. Baker, H.M. Farkas, H.R. Dullin, J. Thomae, J.D. Fay, J.D. Fay, J.F. Mestre, J.I. Hutchinson, K. Koike, L. Fuchs, M. Bershadsky, M. Bershadsky, N.S. Hawley, O. Bolza, P.A. Deift, R. Miranda, T. Grava, V. Z. Enolski, V.G. Knizhnik, V.M. Buchstaber, V.Z. Enolski, W.W. Wirtinger   +37 more
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Boussinesq's equation for water waves: Asymptotics in Sector I

Advances in Nonlinear Analysis
In a recent study, we showed that the large (x,t)\left(x,t) behavior of a class of physically relevant solutions of Boussinesq’s equation for water waves is described by ten main asymptotic sectors.
Charlier Christophe, Lenells Jonatan
doaj   +1 more source

On the long-time asymptotics of the modified Camassa–Holm equation with step-like initial data

European Journal of Applied Mathematics
We study the long-time asymptotics for the solution of the modified Camassa–Holm (mCH) equation with step-like initial data. \begin{align*} &m_{t}+\left (m\left (u^{2}-u_{x}^{2}\right )\right )_{x}=0, \quad m=u-u_{xx}, \\[3pt] & {u(x,0)=u_0(x)\to ...
Engui Fan, Gaozhan Li, Yiling Yang
doaj   +1 more source

The Toda and Painlev\'e Systems Associated with Semiclassical Matrix-Valued Orthogonal Polynomials of Laguerre Type

, 2018
Consider the Laguerre polynomials and deform them by the introduction in the measure of an exponential singularity at zero. In [Chen Y., Its A., J. Approx.
Cafasso, Mattia, de la Iglesia, Manuel D.   +1 more
core   +1 more source

Elliptic Zeta functions and equivariant functions,

, 2017
In this paper we establish a close connection between three notions at- tached to a modular subgroup. Namely the set of weight two meromorphic modular forms, the set of equivariant functions on the upper half-plane commuting with the action of the ...
Al-Shbail, Isra, Sebbar, Abdellah
core   +1 more source

Long-Time Asymptotics for the Korteweg-de Vries Equation via Nonlinear Steepest Descent

, 2008
We apply the method of nonlinear steepest descent to compute the long-time asymptotics of the Korteweg-de Vries equation for decaying initial data in the soliton and similarity region. This paper can be viewed as an expository introduction to this method.
AB Šabat, AM Budylin, AR Its, AR Its, AR Its, AR Its, CS Gardner, Gerald Teschl, GG Varzugin, H Krüger, H Krüger, H Segur, Katrin Grunert, M Klaus, M Wadati, MJ Ablowitz, MJ Ablowitz, NI Muskhelishvili, NJ Zabusky, P Deift, P Deift, P Deift, P Deift, P Deift, P Deift, P Schuur, PA Deift, R Beals, R Hirota, S Tanaka, S Tanaka, SV Manakov, VA Marchenko, VE Zakharov, VS Buslaev, VS Buslaev, W Eckhaus, W Eckhaus, X Zhou   +38 more
core   +4 more sources

Pöschl-Teller potentials based solution to Hilbert's tenth problem

Ingeniería y Ciencia, 2006
Los hipercomputadores computan funciones o números, o en general solucionan problemas que no pueden ser computados o solucionados por una máquina de Turing. Se presenta una adaptación del algoritmo cuántico hipercomputacional propuesto por Tien D.
Andrés Sicard, Juan Ospina
doaj  

A scalar Riemann-Hilbert problem on the torus: applications to the KdV equation. [PDF]

Anal Math Phys, 2022
Piorkowski M, Teschl G.
europepmc   +1 more source

Geometry and analytic theory of Frobenius manifolds

, 1998
Main mathematical applications of Frobenius manifolds are in the theory of Gromov - Witten invariants, in singularity theory, in differential geometry of the orbit spaces of reflection groups and of their extensions, in the hamiltonian theory of ...
Dubrovin, Boris
core   +2 more sources

The nonlinear Schrödinger equation on the half-line with homogeneous Robin boundary conditions. [PDF]

Proc Lond Math Soc, 2023
Lee JM, Lenells J.
europepmc   +1 more source