Riemann–Hilbertov pristup polariziranim solitonima u sredstvu s tri nivoa

Solitons due to the interaction of polarized waves in optically nonlinear media have been analysed using the Riemann-Hilbert transform. We consider the propagation and interaction of differently polarized two-frequency ultrashort optical pulses in a resonant medium consisting of three-level particles. The exact form of the solitons is obtained explicitly.Uporabom Riemann–Hilbertove transformacije proučavaju se solitoni nastali međudjelovanjem polariziranih valova u optički nelinearnom sredstvu. Određena su egzaktna solitonska rješenja za širenje i međudjelovanje dvo–frekventnih ultrakratkih optičkih pulseva različitih polarizacija u rezonantnom sredstvu sa česticama na tri nivoa

On the Effect of Electron Streaming and Existence of Quasi-Solitary Mode in a Strongly Coupled Quantum Dusty Plasma—Far and Near Critical Nonlinearity

A strongly coupled quantum dusty plasma consisting of electrons and dust with the ions in the background is considered when there is streaming of electrons. It is observed that the streaming gives rise to both the slow and fast modes of propagation. The nonlinear mode is then analyzed by the reductive perturbation approach, resulting in the KdV-equation. In the critical situation where non-linearity vanishes, the modified scaling results in the MKdV equation. It is observed that both the KdV and MKdV equations possess quasi-solitary wave solution, which not only has the character of a soliton but also has a periodic nature. Such types of solitons are nowadays called nanopteron solitons and are expressed in terms of cnoidal-type elliptic functions.</jats:p

Solitonska rješenja nelokalne K-P jednadžbe

We have analysed the formation and modulation of solitary waves for the new nonlinear equations - the non-local Kadomstev - Petviashvillee equation, with the help of multiple-scale Fourier transform technique. This equation is a generali¬zation of both the BO equation and KdV equation in three dimensions. We have obtained the equation satisfied by the modulated amplitude and hence the corresponding solitary wave solutions.Pomoću višestruko baždarske Fourierove tehnike analizirali smo formiranje i modulaciju solitonskih valova kod nelinearne i nelokalne jednadžbe Kadomstev-Petviashvilleea. Ta jednadžba je generalizacija BO i KdV jednadžbe na tri dimenzije. Mi smo dobili jednadžbu koju zadovoljava amplitudno modulirani solitonski val

On the Effect of Electron Streaming and Existence of Quasi-Solitary Mode in a Strongly Coupled Quantum Dusty Plasma—Far and Near Critical Nonlinearity

A strongly coupled quantum dusty plasma consisting of electrons and dust with the ions in the background is considered when there is streaming of electrons. It is observed that the streaming gives rise to both the slow and fast modes of propagation. The nonlinear mode is then analyzed by the reductive perturbation approach, resulting in the KdV-equation. In the critical situation where non-linearity vanishes, the modified scaling results in the MKdV equation. It is observed that both the KdV and MKdV equations possess quasi-solitary wave solution, which not only has the character of a soliton but also has a periodic nature. Such types of solitons are nowadays called nanopteron solitons and are expressed in terms of cnoidal-type elliptic functions

Cryptography, Delayed Dynamical Systems, and Secure Communication

The idea of using synchronized chaotic circuits for sending and receiving signals when they are masked using classical cryptography is extended to the case of delayed dynamical systems. It is observed that due to the existence of the delayed parameter t, the mode of communication is more secure due to the fact that the delayed parameter is changed at a fixed interval by both the sender and receiver. It is shown how an extended set of secret keys could be constructed to send a message containing both numerical and alphabetical sequences. Again, a secure communication scheme is also discussed based on the synchronization of two coupled delayed dynamical systems with a varying coupling parameter.</jats:p

Quantum integrable systems

This book presents and clarifies the developments of the last ten years in quantum integrable systems. After a preliminary discussion of the fundamentals of classical nonlinear integrable systems, the authors explore the quantum domain. Their approach emphasizes physical systems and the use of concrete examples, and they take care to establish the relationship between new and older methods. The presentation includes the first comprehensive discussion of the quantum Bäcklund transformation Q-operator and various techniques related to algebraic Bethe Ansatz that are not available elsewhere in book form

Modulational Stability of Envelope Soliton in a Quantum Electron-Ion Plasma in Three Dimension - A generalised Nonlinear Schr ̈odinger Equ ation in 3D

Modulational stability of envelope soliton is studied in a quantum dusty plasma in three dimension.&lt;br&gt;The Krylov-Bogoliubov-Mitropolsky method is applied to the three dimension plasma governing&lt;br&gt;equations. A generalised form of Nonlinear Schr¨odinger equation is obtained whose dispersive term&lt;br&gt;has a tensorial character. Stability condition is deduced abintio and the stability zones are plotted&lt;br&gt;as a function of plasma parameters</jats:p