The current paper recovers dispersive optical solitons in birefringent fibers that are modeled by the Schrödinger–Hirota equation with differential group delay and white noise. Itô Calculus conducts preliminary analysis. G′/G-expansion approach enhanced Kudryashov’s scheme gave way to a wide spectrum of soliton solutions noise component reflected phase soliton.

The theory of fractional calculus goes back to the beginning of the theory of di erential calculus but its inherent complexity postponed the application of the associated concepts. In the last decade the progress in the areas of chaos and fractals revealed subtle relationships with the fractional calculus leading to an increasing interest in the development of the new paradigm. In the area of a...

The Lie derivative, and Exterior Calculus in general, is ubiquitous in the elegant geometric interpretation of many dynamical systems. We extend recent trends towards a Discrete Exterior Calculus by introducing a discrete framework for the Lie derivative defined on differential forms, including a WENO based numerical scheme for its implementation. The usefulness of this operator is demonstrated...

We will ask the question of whether or not the Regge calculus (and two related simplicial formulations) is a consistent approximation to General Relativity. Our criteria will be based on the behaviour of residual errors in the discrete equations when evaluated on solutions of the Einstein equations. We will show that for generic simplicial lattices the residual errors can not be used to disting...

We obtain a discrete time analog of E. Noether’s theorem in Optimal Control, asserting that integrals of motion associated to the discrete time Pontryagin Maximum Principle can be computed from the quasiinvariance properties of the discrete time Lagrangian and discrete time control system. As corollaries, results for first-order and higher-order discrete problems of the calculus of variations a...

In 1980’s, Lee proposed an energy-preserving discrete mechanics with variable time steps by taking (discrete) time as dynamical variable [2, 3, 4]. On the other hand, motivated by the symplectic property of Lagrangian mechanics, a version of discrete Lagrangian mechanics has been devoloped and variational integrators that preserve discrete symplectic two form have been obtained [11, 12, 15, 16,...

The paper aims to identify hidden Markov model parameters. unobservable state represents a finite-state jump process. observations contain Wiener noise with state-dependent intensity. identified parameters include the transition intensity matrix of system state, conditional drift and diffusion coefficients in observations. We propose an iterative identification algorithm based on fixed-interval...

Abstract The main purpose of the presented paper is to obtain some time scale inequalities for different divergences and distances by using weighted scales Jensen’s inequality. These results offer new in h -discrete calculus quantum extend known literature. lower bounds divergence measures are also presented. Moreover, obtained discrete given light Zipf–Mandelbrot law Zipf law.

Grishin ([9]) proposed enriching the Lambek calculus with multiplicative disjunction (par) and coresiduals. Applications to linguistics were discussed by Moortgat ([14]), who spoke of the Lambek-Grishin calculus (LG). In this paper, we adapt Girard’s polarity-sensitive double negation embedding for classical logic ([7]) to extract a compositional Montagovian semantics from a display calculus fo...