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Approximate Methods for Solving Degenerate Singular Integral Equations
AbstractSingular integral equations in degenerate cases describe many processes in natural science and technology. The theory of these equations has...
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Singular Integral Equations
The construction of exact solutions for radiative transfer equations is always based on the transformation of these equations into new ones, for...
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Approximate Methods for Solving Singular Integral Equations in Exceptional Cases
AbstractMultiple processes in physics and technology are simulated using singular integral equations in exceptional cases, which necessitates...
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Path integral and winding number in singular magnetic field
We study a system of identical particles in a singular magnetic field by path integral molecular dynamics. We analytically solve the problem for the...
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A Novel Difference-Integral Equation Satisfied Asymptotically by the Riemann Zeta Function
In 2009 Fokas began a program of study of the investigation of the large t-asymptotics of the Riemann zeta function,...
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An Iterative Scheme for Solving a Lippmann–Schwinger Nonlinear Integral Equation by the Galerkin Method
AbstractThe purpose of this study is to solve a nonlinear integral equation describing the propagation of electromagnetic waves in a body located in...
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On the integral solution of elliptic Kepler’s equation
In a recent paper, Philcox, Goodman and Slepian obtain an explicit solution of the elliptic Kepler’s equation (KE) as a quotient of two contour...
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The \(\sqrt {\epsilon }\) -Law, the Nonlinear H-Equation, and Matrix Singular Integral Equations
For scalar scattering problems, we showed in Part I that many exact results for semi-infinite media can be derived with the so-called resolvent...
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New semi-analytical solution of fractional Newell–Whitehead–Segel equation arising in nonlinear optics with non-singular and non-local kernel derivative
In this paper, a combined form of Laplace transform is applied with the Adomian Decomposition technique for the first time to obtain new...
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Theory of Classical Gaseous Polytropes in an Integral Representation. I. Some General Results
The well known results of the theory of classical gaseous polytropes are presented in the framework of an integral approach where the standard...
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Other Singular Problems
In this chapter we consider methods which solve singular perturbationSingular perturbation problems which may not have boundary layers.
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Boundary Integral Equation Method for 3D Elastodynamic Problems with Chain-Arranged Rigid Disk-Shaped Inclusions
Boundary integral formulation of 3D problems on the normal incidence of time-harmonic longitudinal elastic wave on a one-periodic array of coplanar...
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Soliton patterns in the truncated M-fractional resonant nonlinear Schrödinger equation via modified Sardar sub-equation method
This article explores a noteworthy nonlinear model, namely the truncated M-fractional resonant nonlinear Schrödinger equation (RNLSE), incorporating...
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Trace Formulas for a Complex KdV Equation
AbstractFaddeev and Zakharov determined the trace formulas for the KdV equation with real initial conditions in 1971. We reprove these results for...
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Gaussian Fluctuations for Interacting Particle Systems with Singular Kernels
We consider the asymptotic behaviour of the fluctuations for the empirical measures of interacting particle systems with singular kernels. We prove...
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Exact traveling wave solutions of (2+1)-dimensional extended Calogero–Bogoyavlenskii–Schiff equation using extended trial equation method and modified auxiliary equation method
The (2+1)-dimensional extended Calogero–Bogoyavlenskii–Schiff equation appears in the mathematical description of physical phenomena in plasma...
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Solving the modified Camassa–Holm equation via the inverse scattering transform
AbstractWith the aid of the reciprocal transformation and the associated equation, we study the inverse scattering transform with a matrix...
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Analytic auxiliary mass flow to compute master integrals in singular kinematics
The computation of master integrals from their differential equations requires boundary values to be supplied by an independent method. These...
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Singular products and universality in higher-derivative conformal theory
I investigate universality of the two-dimensional higher-derivative conformal theory using the method of singular products. The previous results for...