Multisoliton solutions and integrability aspects of coupled nonlinear Schrodinger equations

Using Painleve singularity structure analysis, we show that coupled higher-order nonlinear Schrodinger (CHNLS) equations admit Painleve property. Using the results of Painleve analysis, we succeed in Hirota bilinearizing the CHNLS equations, one soliton and two soliton solutions are explictly obtained. Lax pairs are explictly constructed.Comment: Eight pages and six figures. Physical Review E (to be appear

The Sasa-Satsuma higher order nonlinear Schrodinger equation and its bilinearization and multi-soliton solutions

Higher order and multicomponent generalizations of the nonlinear Schrodinger equation are important in various applications, e.g., in optics. One of these equations, the integrable Sasa-Satsuma equation, has particularly interesting soliton solutions. Unfortunately the construction of multi-soliton solutions to this equation presents difficulties due to its complicated bilinearization. We discuss briefly some previous attempts and then give the correct bilinearization based on the interpretation of the Sasa-Satsuma equation as a reduction of the three-component Kadomtsev-Petvishvili hierarchy. In the process we also get bilinearizations and multi-soliton formulae for a two component generalization of the Sasa-Satsuma equation (the Yajima-Oikawa-Tasgal-Potasek model), and for a (2+1)-dimensional generalization.Comment: 13 pages in RevTex, added reference

Detection and attribution of human influence on regional precipitation

Understanding how human influence on climate is affecting precipitation around the world is immensely important for defining mitigation policies, and for adaptation planning. Yet despite increasing evidence for the influence of climate change on global patterns of precipitation, and expectations that significant changes in regional precipitation should have already occurred as a result of human influence on climate, compelling evidence of anthropogenic fingerprints on regional precipitation is obscured by observational and modelling uncertainties and is likely to remain so using current methods for years to come. This is in spite of substantial ongoing improvements in models, new reanalyses and a satellite record that spans over thirty years. If we are to quantify how human-induced climate change is affecting the regional water cycle, we need to consider novel ways of identifying the effects of natural and anthropogenic influences on precipitation that take full advantage of our physical expectations

Studies on some nonlinear schrodinger type equations describing pulse propagation through optical fibers

The discovery of the soliton is considered to be one of the most significant events of the twentieth century. The term soliton refers to special kinds of waves that can propagate undistorted over long distances and remain unaffected even after collision with each other. Solitons have been studied extensively in many fields of physics. In the context of optical fibers, solitons are not only of fundamental interest but also have potential applications in the field of optical fiber communications. This thesis is devoted to the theoretical study of soliton pulse propagation through single mode optical fibers.Cochin University of Science and TechnologDepartment of Physics, Cochin University of Science and Technolo

Optical soliton with damping and frequency chirping in fibre media

Nonlinear Schrodinger (NLS) equation which governs the propagation of single field in the fibre medium with pulse chirping and gain (loss) is considered. The integrability condition of NLS equation is arrived from the linear eigenvalue problem and is studied by using the Painlevé singularity structure analysis. From the Lax pair, soliton solution is constructed by using the Darboux-Bäcklund transformation technique. From the results, we show that the soliton is alive, i.e., pulse area is conserved with the inclusion of damping and pulse chirping effects