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## Meet the editors

Dr. Nalan Antar is a Professor of Applied Mathematics, Department of Mathematical Engineering, Istanbul Technical University, Turkey. She received her Ph.D. in Mechanics from the same university in 1999. She completed her post-doctoral studies at the Department of Mathematics and Statistics, University of Alberta, Canada, and later participated in academic research projects at the University of Colorado at Boulder, USA. She has

published thirty-two research papers in peer-reviewed journals, thirteen conference proceedings, and one book chapter in the fields of nonlinear wave propagation in arteries, optical solitons in nonlinear optics, and water waves problems, in particular gravity currents. She has also edited one book, *Nonlinear Optics - From Solitons to Similaritons*. She has supervised many graduate students in applied mathematics. Dr. Antar is a member of the Scientific Committee of the Turkish National Committee of Theoretical and Applied Mechanics (TUMTMK).

Dr. İlkay Bakırtaş is a Professor of Applied Mathematics, Department of Mathematics, Istanbul Technical University (ITU), Turkey. She received her Ph.D. in Mechanics from the same university in 2003. She completed her postdoctoral studies at the University of Colorado at Boulder, USA. She has published eighteen research papers in peer-reviewed journals, four book chapters, and twenty-one conference proceedings in the fields

of perturbation methods, nonlinear wave propagation in arteries, optical solitons and wave collapse in optics, and water waves problems. She is the editor of the books *Perturbation Methods with Applications in Science and Engineering* and *Nonlinear Optics - From Solitons to Similaritons*. Dr. Bakırtaş is a member of the Scientific Committee of the Turkish National Committee of Theoretical and Applied Mechanics (TUMTMK). She was awarded the 2004 Dr. Serhat Ozyar Young Scientist of the Year Award and the 2003 Best Ph.D. Dissertation Award from TUMTMK.

Contents

**Preface XI**

**Chapter 1 1**

**Chapter 2 19**

**Chapter 3 31**

**Chapter 4 53**

**Chapter 5 69**

**Chapter 6 87**

**Chapter 7 115** Nonlinear Generalized Schrödinger's Equations by Lifting Hamilton-Jacobi's

**Chapter 8 131**

Perspective Chapter: Lattice Solitons in a Nonlocal Nonlinear Medium

*by Mahmut Bağcı, Theodoros P. Horikis, İlkay Bakırtaş and Nalan Antar*

Soliton Like-Breather Induced by Modulational Instability in a Generalized

A Comparison of the Undetermined Coefficient Method and the Adomian Decomposition Method for the Solutions of the Sasa-Satsuma Equation

Resonant Optical Solitons in (3 + 1)-Dimensions Dominated by Kerr Law

Traveling Wave Solutions and Chaotic Motions for a Perturbed Nonlinear Schrödinger Equation with Power-Law Nonlinearity and Higher-Order

*by Mati Youssoufa, Ousmanou Dafounansou, Camus Gaston Latchio Tiofack* 

with Self-Focusing and Self-Defocusing Quintic Nonlinearity

Nonlinear Schrödinger Equation

and Parabolic Law Nonlinearities

*by Khalil S. Al-Ghafri*

*and Alidou Mohamadou*

*by Lothar Moeller*

*by Gérard Gouesbet*

*by Francis T.S. Yu*

*by Mir Asma*

Dispersions

*by Saïdou Abdoulkary and Alidou Mohamadou*

Non-Manakovian Propagation in Optical Fiber

From Schrödinger Equation to Quantum Conspiracy

Formulation of Classical Mechanics

## Contents


*by Francis T.S. Yu*

Preface

The nonlinear Schrödinger equation is a well-known equation that arises for a wide range of scientific purposes, including optical fiber communication systems, quantum mechanics, thermodynamics, ocean acoustic performance, biomedical

This book is a collection of selectively chosen chapters written by some of the world's leading researchers in quantum mechanics and nonlinear optics, particu-

In this book, we present exact and numerical solutions to the nonlinear Schrödinger

Chapter 1 investigates the existence and stability properties of fundamental lattice solitons in a nonlocal nonlinear medium with self-focusing and self-defocusing

In Chapter 2, linear stability analysis is used to study the modulation instability gain for a generalized nonlinear Schrödinger equation with rational nonlinear

Chapter 3 presents different types of soliton solutions, such as bright, dark, singular, and W-shaped solitons, for the extended non-trivial version of the nonlinear Schrödinger equation. The Adomian decomposition method is used to compare the

In Chapter 4, the Projective Riccati equation technique is used to find various types of exact resonant optical soliton solutions, such as bright, dark, singular, king, dark-singular, and combined singular solitons, for the (3 + 1) dimensional resonant

Chapter 5 investigates the existence and stability properties of traveling wave solutions for the perturbed nonlinear Schrödinger equation with power-law nonlinearity

Chapter 6 discusses the non-Manakovian transmission phenomena for nonlinear depolarization of light governed by coupled nonlinear Schrödinger equation in

Chapter 7 presents a set of generalized Schrödinger's equations using the Hamilton– Jacobi equation and lifting principle. The classical Schrödinger's equation is demon-

soliton solutions obtained using the indeterminate coefficient method.

nonlinear Schrödinger equation with Kerr and parabolic nonlinearities.

and higher-order dispersions in a nano-optical fiber.

strated to be the simplest of this set.

dynamics, and quantum physics.

quintic nonlinearity.

terms.

optical fiber.

equation and its applications from various perspectives.

larly concerning the nonlinear Schrödinger equation.
