In this paper, we study an inhomogeneous Hilbert boundary value problem with a finite index and condition on circle for generalized Cauchy-Riemann equation singular coefficient. To solve problem, conducted complete of the solvability theory analytic functions infinite due to number points special type vorticity. Based these results, have derived formula general solution studied existence soluti...

In this paper, the Schwarz boundary value problem (BVP) for the inhomogeneous Cauchy-Riemann equation in a triangle is investigated explicitly. Firstly, by the technique of parquetingreflection and the Cauchy-Pompeiu representation formula a modified Cauchy-Schwarz representation formula is obtained. Then, the solution of the Schwarz BVP is explicitly solved. In particular, the boundary behavio...

Abstract. In the present paper we are concerned with the Novikov–Veselov equation at negative energy, i.e. with the (2+1)–dimensional analog of the KdV equation integrable by the method of inverse scattering for the two–dimensional Schrödinger equation at negative energy. We show that the solution of the Cauchy problem for this equation with non–singular scattering data behaves asymptotically a...

In this paper we obtain explicit lower bounds for the radius of convergence of the Painlevé expansions of the Korteweg-de-Vries equation around a movable singularity manifold S in terms of the sup norms of the arbitrary functions involved. We use this estimate to prove the well-posedness of the singular Cauchy problem on S in the form of continuous dependence of the meromorphic solution on the ...

This manuscript presents a method for the numerical solution of the Cauchy type singular integral equations of the first kind, over a finite segment which is bounded at the end points of the finite segment. The Chebyshev polynomials of the second kind with the corresponding weight function have been used to approximate the density function. The force function is approximated by using the Chebys...