Related papers: Generalized spheroidal wave equation and limiting …
This paper presents a new approach for the computation of eigenvalues of the generalized spheroidal wave equations. The novelty of the present method is in the use of the analytical derivatives of the eigenvalues to minimize losses in…
In recent times it has been paid attention to the fact that (linear) wave equations admit of "soliton-like" solutions, known as Localized Waves or Non-diffracting Waves, which propagate without distortion in one direction. Such Localized…
The time-dependent Maxwell system describing electromagnetic wave propagation in inhomogeneous isotropic media in the one-dimensional case reduces to a Vekua-type equation for bicomplex-valued functions of a hyperbolic variable, see…
The theory of integrable systems of Hamiltonian PDEs and their near-integrable deformations is used to study evolution equations resulting from vertical-averages of the Euler system for two-layer stratified flows in an infinite 2D channel.…
The well-known Regge-Wheeler equation describes the axial perturbations of Schwarzschild metric in the linear approximation. From a mathematical point of view it presents a particular case of the confluent Heun equation and can be solved…
A simple generalization of the Swift-Hohenberg equation is proposed as a model for the pattern-forming dynamics of a two-dimensional field with two unstable length scales. The equation is used to study the dynamics of surface waves in a…
The paper continues the analysis, started in [1] (Part I,arXiv:2302.04353), of the model open wave-guide problem defined by 2 semi-infinite, rectangular wave-guides meeting along a common perpendicular line. In Part I we reduce the solution…
After the pioneering work by Giovangigli on mathematics of multicomponent flows, several attempts were made to introduce global weak solutions for the PDEs describing the dynamics of fluid mixtures. While the incompressible case with…
Porosity-based models are a viable alternative to classical two-dimensional (2-d) Shallow water Equations (SWE) when the interaction of shallow flows with obstacles is modelled. The exact solution of the Single Porosity (SP) Riemann…
We derive the two-breather solution of the class I infinitely extended nonlinear Schrodinger equation (NLSE). We present a general form of this multi-parameter solution that includes infinitely many free parameters of the equation and free…
It is shown that the regular-at-infinity solution of the 1D Schrodinger equation with the hyperbolic Poschl-Teller (h-PT) potential with integer parameters is expressible in terms of a n-order Heun polynomial in y=thr at an arbitrary…
We present a boundary integral formulation of electromagnetic scattering by homogeneous bodies that are characterized by linear constitutive equations in the frequency domain. By working with the Cartesian components of the electric, E and…
The dynamics of surface waves traveling along the boundary of a liquid medium are changed by the presence of floating plates and membranes, contributing to a number of important phenomena in a wide range of applications. Mathematically, if…
We study generalized solutions of an evolutionary equation related to a densely defined skew-symmetric operator in a real Hilbert space. We establish existence of a contractive semigroup, which provides generalized solutions, and find…
We derive a concise closed-form solution for a linear three-term recurrence relation. Such recurrence relations are very common in the quantitative sciences, and describe finite difference schemes, solutions to problems in Markov processes…
A new set of vector solutions to Maxwell's equations based on solutions to the wave equation in spheroidal coordinates allows laser beams to be described beyond the paraxial approximation. Using these solutions allows us to calculate the…
The solution in hyperspherical coordinates for $N$ dimensions is given for a general class of partial differential equations of mathematical physics including the Laplace, wave, heat and Helmholtz, Schr\"{o}dinger, Klein-Gordon and…
In this paper, two kinds of the exact singular solutions are obtained by the improved homogeneous balance (HB) method and a nonlinear transformation. The two exact solutions show that special singular wave patterns exists in the classical…
We develop a mathematically and physically sound definition of the spectrally-hyperviscous Navier-Stokes equations (SHNSE) on general bounded domains \Omega with zero (no-slip) boundary conditions prescribed on \varGamma=\partial\varOmega.…
The long time behavior of an initial step resulting in a dispersive shock wave (DSW) for the one-dimensional isentropic Euler equations regularized by generic, third order dispersion is considered by use of Whitham averaging. Under modest…