相关论文: Continuous changes of variables and the Magnus exp…
A special purpose solver, based on the Magnus expansion, well suited for the integration of the linear three neutrino oscillations equations in matter is proposed. The computations are speeded up to two orders of magnitude with respect to a…
The solution of pseudo initial value differential equations, either ordinary or partial (including those of fractional nature), requires the development of adequate analytical methods, complementing those well established in the ordinary…
Starting from the classic contraction mapping principle, we establish a general, flexible, variational setting that turns out to be applicable to many situations of existence in Differential Equations. We show its potentiality with some…
A change of variables is introduced to reduce certain nonlinear stochastic evolution equations with multiplicative noise to the corresponding deterministic equation. The result is then used to investigate a stochastic porous medium…
Many iterative optimization algorithms involve compositions of special cases of Lipschitz continuous operators, namely firmly nonexpansive, averaged and nonexpansive operators. The structure and properties of the compositions are of…
A general non-local point transformation for position-dependent mass Lagrangians and their mapping into a "constant unit-mass" Lagrangians in the generalized coordinates is introduced. The conditions on the invariance of the related…
In this work, exact solutions of the nonlinear cubic-quintic Duffing-van der Pol oscillator with variable coefficients are obtained. Two approaches have been applied, one based on the factorization method combined with the Field Method, and…
We present a pedagogical introduction to Floquet-Magnus theory through the classical example of Kapitza's pendulum - a simple system exhibiting nontrivial dynamical stabilization under rapid periodic driving. By deriving the equations of…
A simple version for the extension of the Taylor theorem to the operator functions was found. The expansion was done with respect to a value given by a diagonal matrix for the non-commutative case, and the coefficients are given both by…
Darboux transformations in one independent variable have found numerous applications in various field of mathematics and physics. In this paper we show that the extension of these transformations to two dimensions can be used to decouple…
A generalization of the regular continued fractions was given by Chakraborty and Rao \cite{CR-2003}. For the transformation which generates this expansion and its invariant measure, the Perron-Frobenius operator is given and studied. For…
The stationary Schroedinger equation of the harmonic oscillator is deformed by a Darboux transformation to construct time-dependent potentials with the oscillator profile. The Darboux (supersymmetric or factorization) method is usually…
We prove multidimensional integration by parts formulas for generalized fractional derivatives and integrals. The new results allow us to obtain optimality conditions for multidimensional fractional variational problems with Lagrangians…
Nonlinear integrable equations serve as a foundation for nonlinear dynamics, and fractional equations are well known in anomalous diffusion. We connect these two fields by presenting the discovery of a new class of integrable fractional…
In this paper, we briefly explain the spectral expansion problem for differential operators defined on the entire real line, generated by a differential expression with periodic, complex-valued coefficients.
We study a non-autonomous, non-linear evolution equation on the space of operators on a complex Hilbert space. We specify assumptions that ensure the global existence of its solutions and allow us to derive its asymptotics at temporal…
The Fokker-Planck equations describe time evolution of probability densities of stochastic dynamical systems and are thus widely used to quantify random phenomena such as uncertainty propagation. For dynamical systems driven by non-Gaussian…
We have shown that a Lagrangian for a torus surface can yield second order nonlinear differential equations using the Euler-Lagrange formulation. It is seen that these second order nonlinear differential equations can be transformed into…
We establish a generalization of the Maharam Extension Theorem to nonsingular group actions. We also present an extension of Krengel Representation Theorem of dissipative transformations to nonsingular actions.
Asymptotic expansion of the Fokker-Planck equation in terms of the strength of the fluctuation has been carried out. The mean and the variance of the total kinetic energies of the fission fragments have been calculated and compared with the…