79 citations · 1.2k across the 123 of their papers we have counts for
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General Representation of Nonlinear Green's Function for Second Order Differential Equations Nonlinear in the First Derivative
Marco Frasca, Asatur Khurshudyan
The Green's function method which has been originally proposed for linear systems has several extensions to the case of nonlinear equations. A recent extension has been proposed to…
Green's functions for higher order nonlinear equations
Marco Frasca, Asatur Zh. Khurshudyan
The well-known Green's function method has been recently generalized to nonlinear second order differential equations. In this paper we study possibilities of exact Green's functio…
A General Representation for the Green's Function of Second Order Nonlinear Differential Equations
Marco Frasca, Asatur Khurshudyan
In this paper we study some classes of second order non-homogeneous nonlinear differential equations allowing a specific representation for nonlinear Green's function. In particula…
Quantum Yang-Mills field theory
Marco Frasca
We show that the Dyson-Schwinger set of equations for the Yang-Mills theory can be exactly solved till the two-point function. This is obtained given a set of nonlinear waves solvi…
Exact solutions for classical Yang-Mills fields
Marco Frasca
We provide a set of exact solutions of the classical Yang-Mills equations. They have the property to satisfy a massive dispersion relation and hold in all gauges. These solutions c…
Numerical proof of existence of fractional powers of Wiener processes
Marco Frasca, Alfonso Farina
Using the Euler--Maruyama technique, we show that a class of Wiener processes exist that are obtained by computing an arbitrary positive power of them. This can be accomplished wit…
Exact solutions and zero modes in scalar field theory
Marco Frasca
We provide a set of exact solutions in field theory of scalar fields with symmetry that involve Jacobi elliptic functions. These solutions have the interesting property to pr…
Probabilistic Turing Machine and Landauer Limit
Marco Frasca
We show the equivalence between a probabilistic Turing machine and the time evolution of a one-dimensional Ising model, the Glauber model in one dimension, equilibrium positions re…
Quantum mechanics is the square root of a stochastic process
Marco Frasca
We prove a theorem showing that quantum mechanics is not directly a stochastic process characterizing Brownian motion but rather its square root. This implies that a complex-valued…
Exact solutions of classical scalar field equations
Marco Frasca
We give a class of exact solutions of quartic scalar field theories. These solutions prove to be interesting as are characterized by the production of mass contributions arising fr…
Dual Lindstedt series and KAM theorem
Marco Frasca
We prove that exists a Lindstedt series that holds when a Hamiltonian is driven by a perturbation going to infinity. This series appears to be dual to a standard Lindstedt series a…
Mapping a Massless Scalar Field Theory on a Yang-Mills Theory: Classical Case
Marco Frasca
We analyze a recent proposal to map a massless scalar field theory onto a Yang-Mills theory at classical level. It is seen that this mapping exists at a perturbative level when the…
Two-dimensional Ricci flow as a stochastic process
Marco Frasca
We prove that, for a two-dimensional Riemannian manifold, the Ricci flow is obtained by a Wiener process.