Related papers: The Complex Bateman Equation
This article handles in a short manner a few Laplace transform pairs and some extensions to the basic equations are developed. They can be applied to a wide variety of functions in order to find the Laplace transform or its inverse when…
Generalized Bargmann representations which are based on generalized coherent states are considered. The growth of the corresponding analytic functions in the complex plane is studied. Results about the overcompleteness or undercompleteness…
In this note we have further developed the study of topologically non-trivial solutions of vacuum electrodynamics. We have discovered a novel method of generating such solutions by applying conformal transformations with complex parameters…
We develop a new and further generalized form of the fractional kinetic equation involving generalized k-Bessel function. The manifold generality of the generalized k-Bessel function is discussed in terms of the solution of the fractional…
We establish a set of relations between several quite diverse types of weighted inequalities involving various integral operators and fairly general quasinorm-like functionals which we call sub-monotone. The main result enables one to solve…
A fairly general expression for a light beam is found as a solution of the paraxial Helmholtz equation. It is achieved by exploiting appropriately chosen complex variables which entail the separability of the equation. Next, the expression…
Iterative equation is an equality with an unknown function and its iterates. There were not found a result on iterative equations with multiplication of iterates of the unknown function on $\mathbb{R}$. In this paper we use an exponential…
A systematic derivation of Boltzmann equation is presented in the framework of closed-time-path formalism. Introducing a new type of probe, the expectation value of number operator is calculated as a functional of source. Then solving for…
A complex notion of backward stochastic differential equation (BSDE) is proposed in this paper to give a probabilistic interpretation for linear first order complex partial differential equation (PDE). By the uniqueness and existence of…
We give new Backlund transformations (BTs) for some known integrable (in the sense of being multidimensionally consistent) quadrilateral lattice equations. As opposed to the natural auto-BT inherent in every such equation, these BTs are of…
A recurrence relations for sums of powers of complex functions can be written as a system of linear equation AX=B. Using properties of determinant and Cramer's rule for solving systems of linear equation, this paper presents an absolutely…
I show that the general implicit-function problem (or parametrized fixed-point problem) in one complex variable has an explicit series solution given by a trivial generalization of the Lagrange inversion formula. I give versions of this…
We consider an ordinary nonlinear differential equation with generalized coefficients as an equation in differentials in algebra of new generalized functions. Then the solution of such equation will be a new generalized function. In the…
These lecture notes highlight the mathematical and computational structure relating to the formulation of, and development of algorithms for, the Bayesian approach to inverse problems in differential equations. This approach is fundamental…
We consider the functional inverse of the Gamma function in the complex plane, where it is multi-valued, and define a set of suitable branches by proposing a natural extension from the real case.
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
The Chapman-Enskog method of solution of the relativistic Boltzmann equation is generalized in order to admit a time-derivative term associated to a thermodynamic force in its first order solution. Both existence and uniqueness of such a…
We introduce a particular nonlinear generalization of quantum mechanics which has the property that it is exactly solvable in terms of the eigenvalues and eigenfunctions of the Hamiltonian of the usual linear quantum mechanics problem. We…
A solution of the Einstein vacuum field equations is constructed within the contex of perturbation theory. The solution possesses a graphical representation in terms of diagrams.
In view of the role of reaction equations in physical problems, the authors derive the explicit solution of a fractional reaction equation of general character, that unifies and extends earlier results. Further, an alternative shorter…