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We propose a method to calculate wave functions and energies not only of the ground state but also of low-lying excited states using a deep neural network and the unsupervised machine learning technique. For systems composed of identical…
We give some supersymmetric wave solutions, both chiral (selfdual) and nonchiral, to interacting supersymmetric theories in four dimensions.
The challenging nuclear many-body problem is discussed along with classifications and qualitative descriptions of existing methods and models. We present detailed derivations of a new method where cluster correlations co-exist with an…
This article addresses linear hyperbolic partial differential equations with non-smooth coefficients and distributional data. Solutions are studied in the framework of Colombeau algebras of generalized functions. Its aim is to prove upper…
We reveal the existence of a new type of surface electromagnetic waves supported by hyperbolic metasurfaces, described by a conductivity tensor with an indefinite signature. We demonstrate that the spectrum of the hyperbolic metasurface…
Uniform asymptotic approximations are obtained for the prolate spheroidal wave functions, in the high-frequency case. The results are obtained by an application of certain existing asymptotic solutions of differential equations, and involve…
In this paper, we will consider generalised eigenfunctions of the Laplacian on some surfaces of infinite area. We will be interested in lower bounds on the number of nodal domains of such eigenfunctions which are included in a given bounded…
We consider the statistics of the number of nodal domains aka nodal counts for eigenfunctions of separable wave equations in arbitrary dimension. We give an explicit expression for the limiting distribution of normalised nodal counts and…
We develop a weakly nonlinear model to study the spatiotemporal manifestation and the dynamical behavior of surface waves in the presence of an underlying interfacial solitary wave in a two-layer fluid system. We show that interfacial…
A numerical method to build an orthonormal basis of properly symmetrized hyperspherical harmonic functions is developed. As a part of it, refined algorithms for calculating the transformation coefficients between hyperspherical harmonics…
A new analytical approach to description of electromagnetic waves in nonmagnetic anisotropic media is presented. Amplitudes of their reflection and refraction at interfaces and also reflection and transmission of plane parallel plates are…
We introduce a theory of optical responses of bianisotropic layers with arbitrary effective medium parameters, which results in generalized Fresnel-Airy equations for reflection and transmission coefficients at all incidence directions and…
The physical consistency of the match of piecewise-$C^0$ metrics is discussed. The mathematical theory of gravitational discontinuity hypersurfaces is generalized to cover the match of regularly discontinuous metrics. The mean-value…
We study the hierarchical wave functions on a sphere and on a torus. We simplify some wave functions on a sphere or a torus using the analytic properties of wave functions. The open question, the construction of the wave function for…
The nodal surfaces of the many-body wavefunction are fundamental geometric features that encode critical information regarding particle statistics and their interaction. Directly probing these structures, particularly in correlated quantum…
A method is proposed to find the wave function of an electron moving infinitely in the field of an arbitrary 1D layer structure with two different homogeneous semi-infinite boundaries. It is shown that in general the problem reduces to…
We present the general analytical theory for Dyakonov surface waves at the interface of a biaxial anisotropic dielectric with an isotropic medium. We demonstrate that these surface waves can be divided into todo distinct classes, with…
The nonlinear dynamics of the free surface of an ideal dielectric liquid in a strong electric field is studied. The equation for the evolution of surface electrohydrodynamic waves is derived in the approximation of small surface-slope…
This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integro-differential equations with bounded and measurable coefficients. The…
This paper aims at developing new shape functions adapted to smooth vanishing coefficients for scalar wave equation. It proposes the numerical analysis of their interpolation properties. The interpolation is local but high order convergence…