Related papers: Schlesinger transformations for algebraic Painleve…
We develop the differential theory of complex spinorial forms associated with irreducible complex spinors across all dimensions and signatures. This framework enables the study of constrained parallelicity conditions for irreducible complex…
The transformation theory of the Appell $F_2(a,b_1,b_2;c_1,c_2;x,y)$ double hypergeometric function is used to obtain a set of series representations of $F_2$ which provide an efficient way to evaluate $F_2$ for real values of its arguments…
We introduce and study the dynamics of Chebyshev polynomials on $d>2$ real intervals. We define isoharmonic deformations as a natural generalization of the Chebyshev dynamics. This dynamics is associated with a novel class of constrained…
Painleve transcendents are usually considered as complex functions of a complex variable, but in applications it is often the real cases that are of interest. Under a reasonable assumption (concerning the behavior of a dynamical system…
We consider a generating set of reparametrization invariants that can be constructed from the couplings and masses entering the scalar potential of the general Two-Higgs-Doublet Model (2HDM). Being independent of higgs-basis rotations, they…
We apply the spiralling branes technique introduced in arXiv:2312.16990 to many-body integrable systems. We start by giving a new R-matrix description of the trigonometric Ruijsenaars-Schneider (RS) Hamiltonians and eigenfunctions using the…
We consider a Pfaffian system expressing isomonodromy of an irregular system of Okubo type, depending on complex deformation parameters u=(u_1,...,u_n), which are eigenvalues of the leading matrix at the irregular singuilarity. At the same…
An exactly solvable position-dependent mass Schr\"odinger equation in two dimensions, depicting a particle moving in a semi-infinite layer, is re-examined in the light of recent theories describing superintegrable two-dimensional systems…
Recasting the $N$-point one loop scalar integral from Feynman to Schwinger parameters gives an integrand with a Gaussian form. By application of a Fourier transform, it is easy to derive explicit expressions for the two, three and…
Fokker-Planck PDEs (incl. diffusions) for stable L\'{e}vy processes (incl. Wiener processes) on the joint space of positions and orientations play a major role in mechanics, robotics, image analysis, directional statistics and probability…
Assuming that there exist at least two fermionic parameters, the classical N= 1 supersymmetric Korteweg-de Vries (SKdV) system can be transformed to some coupled bosonic systems. The boson fields in the bosonized SKdV (BSKdV) systems are…
The Painleve expansion for the second Painleve equation (PII) and fourth Painleve equation (PIV) have two branches. The singular manifold method therefore requires two singular manifolds. The double singular manifold method is used to…
The inverse problem of the calculus of variations consists in determining if the solutions of a given system of second order differential equations correspond with the solutions of the Euler-Lagrange equations for some regular Lagrangian.…
The Schlesinger equations $S_{(n,m)}$ describe monodromy preserving deformations of order $m$ Fuchsian systems with $n+1$ poles. They can be considered as a family of commuting time-dependent Hamiltonian systems on the direct product of $n$…
Rational solutions of the inhomogeneous Painleve-II equation and of a related coupled Painleve-II system have recently arisen in studies of fluid vortices and of the sine-Gordon equation. For the sine-Gordon application in particular it is…
We exhibit a remarkable connection between sixth equation of Painleve list and infinite families of explicitly uniformizable algebraic curves. Fuchsian equations, congruences for group transformations, differential calculus of functions and…
We present new infinitesimal `conformal-like' symmetries for the field equations of strictly massless spin-$s \geq 3/2$ totally symmetric tensor-spinors (i.e. gauge potentials) on 4-dimensional de Sitter spacetime ($dS_{4}$). The…
The Painleve first equation can be represented as the equation of isomonodromic deformation of a Schrodinger equation with a cubic potential. We introduce a new algorithm for computing the direct monodromy problem for this Schrodinger…
We present FastLSQ, a framework for PDE solving and inverse problems built on trigonometric random Fourier features with exact analytical derivatives. Trigonometric features admit closed-form derivatives of any order in $\mathcal{O}(1)$,…
Starting with a Riccati equation solved by hypergeometric functions, some sequences of rational solutions to Painleve' VI are obtained.