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Archive for the ‘Planck’s Formula’ Category

The nonlinear Schrödinger equation (NSE) has served as the governing equation of optical soliton in the study of its applications to optical communication and optical switching. Various schemes have been employed for the solution of this nonlinear equation as well as its variants. We report in this paper a relatively simpler new approach for the analytic solution of NSE. In this scheme the equation was first transformed into an arctangent differential equation, which was then separated into the linear and nonlinear parts, with the linear part solved in a straight forward manner. The solution of the nonlinear equation was written in the form of modulation function characterized by its amplitude function A and phase function F(A). Substituting the linear solution for A, the arctangent differential equation was solved for a certain initial value of A. It is shown that this method is applicable to other first-order nonlinear differential equation such as the Korteweg de Vries equation (KdV), which can be transformed into an arctangent differential equation.

I. Introduction

The phenomenon of the solitary wave propagation was observed for the first time by the Scottish scientist John Scott Russell in 1844, when one day he was watching water waves of a certain shape kept on traveling without changing their shape for a distance as far as his eye could see. To explain the behavior of such unusual wave, Korteweg and de Vries governed a model for the wave propagation in shallow water in form a partial differential equation called as KdV differential equation, which its solution appropriates to the features of the solitary wave called as soliton[1]. The existence of solitons in optical fiber was predicted by Zakarov and Zabat (1972) after they derived a differential equation for the light propagating in an optical fiber, that demonstrated later by Hazagawa in 1973 at Bell Laboratory. Next, Mollenauer and Stolen employed the solitons in optical fiber for generating subpicosecond pulses.

For Detail Visit :

  1. New Science Future (http://rohedi.blogspot.com)
  2. ROHEDI Laboratory (http://rohedi.com)
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A New Planck’s Formula of Spectral Density of Black-body Radiation by Means of AF(A) Diagram

A New Planck’s Formula of Spectral Density of Black-body Radiation by Means of AF(A) Diagram

This paper reports derivation of a new Planck’s formula of spectral density of black-body radiation, that was originated by modeling the interpolation formula of Planck’s law of obtaining the mean of energy of black-body cavity in 2nd order of Bernoulli equation. The new Planck’s formula is created by means AF(A) diagram of solving arctangent differential equation after transforming the Bernoulli equation into the arctangent differential equation The New Planck’s formula not only contains the terms of the photon energy and the energy difference between two states of the motion of harmonic oscillator (), but also contains both terms of the minimum energy of harmonics oscillator () and the phase differences (ωh2/ωh2/π) as representing the intermodes-orthogonality, hence it can answer why the explanation of black-body radiation has been associated with the harmonic oscillators

For Detail Visit :

  1. New Science Future (http://rohedi.blogspot.com)
  2. ROHEDI Laboratory (http://rohedi.com)

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