**Chapter 6 111**

Approximate Analytical Solution of Nonlinear Evolution Equations *by Laxmikanta Mandi, Kaushik Roy and Prasanta Chatterjee*

Preface

Almost 99 percent of matter in the universe exists in a plasma state, as in the form of the Sun, stars, lightning, welding arcs, interplanetary and interstellar space, and in neon and fluorescent tubes. Plasma is an electrically conducting medium in which there are roughly equal numbers of neutral and positively and negatively

This book introduces topics of plasma physics and presents related applied research. Several chapters deal with basic concepts in plasma physics, nonequilibrium plasma modeling, space plasma applications, and plasma diagnostics. The book also gives an overview of the linear and nonlinear aspects of plasma physics. As such, it is a

The first chapter provides an introduction to plasma physics, occurrence of plasma in universe, types of plasma, plasma quasi-neutrality, plasma frequency, Debye shielding, and waves in plasma. It also discusses stable and unstable plasma oscilla-

Chapter 2 discusses the technological application of plasma physics in the field of electric propulsion. These devices have much greater exhaust velocities, longer lifetime, and greater thrust density than chemical propulsion devices. The chapter discusses different types of plasma propulsion devices by providing mathematical formulations. It also presents the current status of the research on Hall thrusters.

Chapter 3 discusses the interaction of microwave electric fields with plasma. It also gives the dispersion relations of electrostatic and electromagnetic waves. The spatio-temporal evolution pattern of microwave-radiated plasma parameters high-

Chapter 4 deals with the design of smart plasma antennas to achieve high gain and reconfigurable beam width without physically moving the antenna. It also reports

Chapter 5 explains the principles of the diagnostic technique for a test charge in Lorentzian dusty plasma with the help of space-time Fourier transformations. Finally, Chapter 6 deals with the theory of nonlinear waves in plasma to obtain the Korteweg-de Vries (KDV) equation by using the Reductive Perturbation

We are grateful to our authors Rostomyan, Mallick, Bandyopadhyay, R. Kumar, Theodore Anderson, S. Ali, Y. Al-Hadeethi, Laxmikanta Mandi, Kaushik Roy, and Prasanta Chatterjee. I especially thank Mr. Anil Joshi, who always gave me good advice and helped on several occasions. Special thanks to my parents, sisters, grandfather, and wife Rajvinder Kaur for her cooperation in my life and for sharing

useful resource for many young researchers and students in the field.

tions with the help of two fluids, also called plasma hydrodynamics.

light the role of these electric fields in power coupling processes.

on the generation of microwaves and their reflection from plasma.

charged particles.

Technique.
