Analytical Approach in Nonlinear Dispersive Media

This book presents an analytical approach to treating several topics of current interest in the field of nonlinear partial differential equations and their applications to electrical and communications engineering, the physics of nonlinear dispersive media, as well as the nonlinear wave interactions. It treats analytically Ginzburg-Landau and wave equations such as higher-order nonlinear Schrodinger equations with/without dissipative terms, Gross-Pitaevskii equations with complicated potential terms, and cubic-quintic Ginzburg-Landau equations. For solving analytically various problems of mathematical physics in nonlinear dispersive media, the book explanatorily and carefully applies several powerful methods drawn from recent leading research articles. Special attentions are paid to the modulational instability phenomenon and baseband modulational instability phenomenon in nonlinear dispersive media. The theoretical results of this book are supplemented by numerical calculations and graphical illustrations. This book is intended for scientific researchers working in the field of nonlinear waves; it will be particularly useful for applied mathematicians, theoretical physicists, as well as electrical and communications engineers.

1. Modulational instability of one-component Bose-Einstein condensate.- 2. Matter-wave solitons of Bose-Einstein condensates in periodic potentials.- 3. Modulational instability and soliton interactions in Bose-Einstein condensates.- 4. Engineering localized waves in Gross-Pitaevskii equations with time-dependent trapping potentials.- 5. Baseband modulational instability and interacting localized mixed waves in nonlinear media.

Emmanuel Kengne obtained his Ph.D. degree in Physico-mathematical Sciences from the School of Mathematics and Mechanical Engineering at Kharkov State University (now Kharkov National University), Ukraine, in January 1994. He is an applied mathematician, full professor at the School of Physics and Electronic Information Engineering, Zhejiang Normal University (China), adjunct professor at the Department of Computer Science and Engineering, University of Quebec at Outaouais (Canada), and adjunct researcher at the Institute of Physics, Chinese Academy of Sciences (China). Emmanuel Kengne has made major contributions to a vast number of fields, including the theory of well-posedness boundary value problems for partial differential equations, wave propagation on nonlinear transmission networks, optical and heat solitons, nonlinear dynamical lattices, Ginzburg-Landau models, Boson-Fermion models, bio-thermal physics, light propagation, thermal therapy for tumors, as well as many other physico-mathematical fields.

Wu-Ming Liu obtained his Ph.D. degree from the Institute of Metal Research, Chinese Academy of Sciences, Shenyang, China, in June 1994. He became an associate professor at the Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, China, in 1996, and is a full professor at the Institute of Physics at the same Academy since 2002.