Darboux transformation is one of the methods used in solving nonlinear evolution equation. Basically, the Darboux transformation is a linear algebra formulation of the solutions of the Zakharov-Shabat system of equations associated with the nonlinear evolution equation. In this work, the evolution of monochromatic electromagnetic wave in a nonlinear-dispersive optical medium is considered. Using the Darboux transformation, explicit multisoliton solutions (one to three soliton solutions) are… Expand

In this article, we construct the Darboux solutions of integrable coupled nonlinear wave equation associated with Hirota Satsuma system in Darboux framework with their N-th generalization in terms of… Expand

We derive exact analytical expressions for the spatial Fourier spectrum of the fundamental bright soliton solution for the ( 1 + 1 ) -dimensional nonlinear Schrödinger equation. Similar to a Gaussian… Expand

In 1882 Darboux proposed a systematic algebraic approach to the solution of the linear Sturm-Liouville problem. In this book, the authors develop Darboux's idea to solve linear and nonlinear partial… Expand

Oxford Master Series in Atomic, Optical, and Laser Physics

2009

TLDR

The intention is to introduce readers at this level to the fundamental, but rather simple, ideas behind ground-breaking developments including quantum cryptography, teleportation and quantum computing.Expand