Hydromagnetic waves - Theory and applications Scientific report

Magnetohydrodynamic wave influence on various physical phenomen

Notes on magnetohydrodynamics, part ii

Simple waves and covariant formulation related to magnetohydrodynamics and derivation of equations for one-dimensional wave propagation and Riemann invariants for fast and slow wave

Distributional solutions of the Wiener-Hopf integral and integro-differential equations

We present the theory and technique for obtaining the distributional solutions for the Wiener-Hopf integral and integro-differential equations. This is achieved by identifying a class of kernels for which these equations are well defined and are of the Fredholm type. Consequently, the associated operators and their images are of finite dimensions. Furthermore, we define the operators in such a way that the corresponding equations hold at the end points; otherwise, the equations are usually ill-behaved. We illustrate our analysis with the help of various examples. © 1991, Rocky Mountain Mathematics Consortium. All Rights Reserved

Some results in discontinuous fields and wave propogation

We present various applications of recently developed techniques which are an interplay between the differential geometry and the theory of distributions. We apply them to the microlocal theory, derive the general order transport equations for the strength of wave fronts, obtain the values of the jumps of the general Nth-order derivatives of the harmonic functions across the potential layers, and present the explicit formulas for an arbitrary order derivative of functions of the radial distance r. © 1987

Regularization, pseudofunction, and hadamard finite part

First, we discuss and correlate the various types of regularizations available in the literature for the singular function H(x) xk, where k is an integer and H(x) is the Heaviside function. Then we present the corresponding regularization for the function r-k, where r is the radial distance in Rn. Thereafter, we express the recently discovered distributional derivatives of this function in terms of pseudofunctional language commonly used in the Coulomb, gravitational, and interparticle potentials where the function 1 r plays a fundamental role. © 1989

Non-classical derivation of the transport theorems for wave fronts

We establish a relationship between the derivatives of generalized functions and the transport theorems for moving surfaces of discontinuity. We study the motion of a propagating and deforming wave front which itself can have a moving discontinuity on its surface. With the help of the theory of generalized derivatives we present a general transport theorem which embodies the known results as special cases. © 1991

The asymptotic expansion of certain multi-dimensional generalized functions

We apply regularization of divergent integrals in the derivation of the asymptotic expansion of certain multi-dimensional generalized functions. We further present several illustrations to demonstrate that the asymptotic development of generalized functions provides a lucid formulation of many concepts in asymptotic analysis such as the expansion of oscillatory integrals and the expansion of certain series. © 1992

Distributional analysis for discontinuous fields

The jump conditions that hold across singular surfaces for the fields having step function discontinuities do not, in general, apply if these surfaces themselves carry concentrated fields. In this note, the general situation when the surfaces of discontinuity carry multilayers and deform as they propagate is discussed. Formulas are presented for the first and second derivatives for these multilayers. © 1985

Distributional boundary values of harmonic and analytic functions

A theory for distributional boundary values of harmonic and analytic functions is presented. In this analysis there arise several indicators that measure the growth of these functions near the boundaries. An extension of the Phragmén-Lindelöf maximum principle is derived. Furthermore, the algebraic properties of the space of real periodic distributions are studied. By introducing a new product, the harmonic product, the boundary conditions involving harmonic functions are transformed into ordinary differential equations. © 1982

Pre-asymptotic expansions

We introduce the concepts of pre-asymptotic schemes and pre-asymptotic expansions to study the divergent series that formally are solutions of various types of equations. © 1996 Academic Press, Inc