Introducing a projection method into a one-dimensional model of a pulse propagation in isotropic media, we derive and investigate a system of equation describing dynamics ultrashort pulses of opposite directions ofpropagation and ones with interaction of directed pulses with different polarization.

In this article, we consider a one-dimensional model of electromagnetic pulse propagation in isotropic media, takinginto account a nonlinearity of the third order. We introduce a method for Maxwell's equation transformation on thebasis of a complete set of projecting operators. The operators correspond to wave dispersion branches including thedirection of propagation. As the simplest result of applying the method, we derive a system...

Ogólna teoria oddziaływania modów hydrodynamicznych opiera się na wyprowadzeniu równań różniczkowych nieliniowych. Mody rozumiane są tu jako wektory własnych układów praw zachowań hydrodynamicznych. Rozpatrywano zjawiska towarzyszące fali akustycznej w przepływie lepkim nieliniowym. Uwzględniono płyny w każdym fizycznym równaniu stanu.

Non-invasive measurement methods offer great benefits in the field of medical diagnostics with molecular-specific techniques such as Raman spectroscopy which is increasingly being used for quantitative measurements of tissue biochemistry in vivo. However, some important challenges still remain for label-free optical spectroscopy to be incorporated into the clinical laboratory for routine testing. In particular, non-analyte-specific...

We present the application of projection operator methods to solving the problem of the propagation and interaction of short optical pulses of different polarizations and directions in a nonlinear dispersive medium. We restrict ourselves by the caseof one-dimensional theory, taking into account material dispersion and Kerr nonlinearity. The construction of operators is delivered in two variants: for the Cauchy problem and for the...