Related papers: The Complex Bateman Equation in a space of arbitra…
A general solution to the Complex Monge-Amp\`ere equation in a space of arbitrary dimensions is constructed.
The general solution to the Complex Bateman equation is constructed. It is given in implicit form in terms of a functional relationship for the unknown function. The known solution of the usual Bateman equation is recovered as a special…
The general solution to the Complex Monge-Amp\`ere equation in a two dimensional space is constructed.
Some special solutions to the multidimensional Lam\'e and Bourlet type equations are constructed in an explicit form.
The multi-field generalisation of the Bateman equation arises from considerations of the continuation of String and Brane equations to the case where the base space is of higher dimension than the target space. The complex extension of this…
In this paper we study solutions of the critical Lane-Emden equation in higher space dimensions. We show that after certain transformations the general solution can be written in terms of elliptic functions. We restrict ourselves to real…
We develop a method to obtain the general solution of the Laplace equation in $d$-dimension in ultraspherical coordinates.
We construct several types of multi-valued solutions to the Monge-Ampere equation in higher dimensions.
Klein-Gordon Equation has been solved in four dimension. The potential has been chosen to be any arbitrary field Potential.
This paper explores the solution of Fredholm-like equations with infinite dimensional solution spaces. We set out to find a method for determining a particular solution to a Fredholm-like equation subject to a given constraint. The…
An infinite-dimensional family of exact solutions of a three-dimensional biharmonic equation was constructed by the hypercomplex method.
We introduce complex intersection bodies and show that their properties and applications are similar to those of their real counterparts. In particular, we generalize Busemann's theorem to the complex case by proving that complex…
Let $X$ be an analytic space of pure dimension. We introduce a formalism to generate intrinsic weighted Koppelman formulas on $X$ that provide solutions to the $\dbar$-equation. We obtain new existence results for the $\dbar$-equation, as…
This paper describes infinite sets of polynomial equations in infinitely many variables with the property that the existence of a solution or even an approximate solution for every finite subset of the equations implies the existence of a…
We derive an explicit formula for the volume of a regular simplex in the hyperbolic space of any dimension.
We consider the characteristic problem for the ultrahyperbolic equation in the Euclidean space. The value of a solution is prescribed on the characteristic hyperplane. A well-posed set-up of the problem is discussed. We obtain a certain…
Since the answer to the complex Busemann-Petty problem is negative in most dimensions, it is natural to ask what conditions on the (n-1)-dimensional volumes of the central sections of complex convex bodies with complex hyperplanes allow to…
Particular solutions of the Benney equations are constructed. Their properties are discussed.
A further class of complex covariant field equations is investigated. These equations possess several common features: they may be solved, or partially solved in terms of implicit functional relations, they possess an infinite number of…
We obtain exact solutions to the class of parabolic partial differential equations of arbitrary dimensionality and with arbitrary potentials. The solutions are presented in a compact-form: as explicit mathematical expressions consisting of…