The extended tanh method with a computerized symbolic computation, is used for constructing the travelling wave solutions of coupled nonlinear equations arising in physics. The obtained solutions include solitons, kinks and plane periodic solutions. The applied method will be used to solve the generalized coupled Hirota Satsuma KdV equation, and seeking soliton solutions of two-component generalizations of the Kaup- Kupershmidt and Sawada-Kotera equations.
A system of microring resonators (MRRs) connected to an optical modified add/drop filter system is used. The optical soliton pulse of 60 GHz frequency band can be generated and used for millimeter waves in radio over fiber (ROF) applications. Wireless Personal Area Network (WPAN) as IEEE 802.15.3c is one of the applications for the ROF. The system uses chaotic signals generated by a Gaussian laser pulse propagating within a nonlinear MRRs system. The chaotic signals can be generated via a series of MRRs. The IEEE 802.15.3c standard operates at the 60 GHz frequency band, and it is applicable for a short distance optical communication such as indoor systems, where the higher transmission data rate can be performed using a high frequency band of the output optical soliton pulses.
This book is focused on nonlinear properties of Gallium nanoparticles. The theoretical model of gallium nanoparticle film at the tip of monomode optical fibre has been developed. The interface problem is solved by phase plane analysis, inverse scattering transform method and equivalent particle theory. Effective dielectric constant of gallium nanoparticles on silica substrate has been calculated using into account the Maxwell-Garnett Effective Medium Theory. Minimum power required for Soliton propagation, Stability, shape and size of soliton have also been calculated. Theoretical results have been obtained by applying the perturbation theory for solitons based on the inverse scattering transform method. These investigations have yielded important new insights into all-optical switching devices, upper and lower threshold devices and memory elements. Soliton switch and directional couplers as an application of reflectivity hysteresis due to structural phase transformation in a thin film of gallium nanoparticles on a silica substrate has also been mentioned in the book.
WHAT IS THE KDV EQUATION?WHAT IS FORCED KDV EQUATION?WHAT IS THE SOLITON? WHAT IS STATIONARY FORCED KDV EQUATION?WHAT IS SOLUTION OF THE FORCED KDV EQUATION?WHAT IS THE SUPERCRITICAL SOLUTION OF THE FORCED KDV EQUATION?THE STUDY OF THE SOLITON IS VERY IMPORTANT WHY? SOLITON WAVE CAN USE IN COMMUNICATIONS HOW?SOLITON WAVE CAN USE IN HAND PHONE HOW? THIS BOOK CAN ANSWER ALL THESE EQUATIONS AND MORE?LET US IN JOIN WITH SOLUTION OF THE FORCED KDV EQUATION?
In this book we study the direct and inverse scattering theory of the Zakharov-shabat system. The direct problem consists of deriving the scattering data (the reflection coefficient, the bound states and the norming constants) starting from the potentials k(x) and l(x). The analytic and continuity properties of the Jost solutions and the scattering data are established in a rigorous way. The inverse scattering theory of determining the potentials when the scattering data are given is formulated in terms of the Marchenko equations. The main problem to get an explicit solution of the Marchenko equations is solved by using matrix triplets. Finally, the Inverse Scattering Transform is applied to solve the initial value problem for the Nonlinear Schr7Foedinger equation (NLS). We derive an explicit solution formula of the NLS equation which includes many of the N-soliton solutions already known in the literature and a new class of solutions: the multipole solutions (corresponding to bound states with algebraic multiplicities greater than one).
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