1st Edition
Darboux Transformation of Nonlinear Schrödinger Equations A Guide and a Tutorial
1. Introduction 2. Darboux Transformation of the Fundamental Nonlinear Schrödinger Equation 3. Darboux Transformation of Higher-Order Nonlinear Schrödinger Equations 4. Darboux Transformation of Coupled Nonlinear Schrödinger Equations 5. Darboux Transformation of Two- and Three-Dimensional Nonlinear Schrödinger Equation 6. Darboux Transformation of a Generalized Nonlinear Schrödinger Equation with Function Coefficients 7. Darboux Transformation of Discrete Nonlinear Schrödinger Equation 8. Darboux Transformation of Nonlocal Nonlinear Schrödinger Equation 9. Lax Pair Search Method 10. Other Integrable Nonlinear Differential Equations Appendix A: Mathematica Codes Appendix B: List of Lax Pairs Presented in this Book Bibliography. Index.
Biography
Laila Al Sakkaf is an Assistant Professor in the Department of Applied Sciences, College of Engineering, at Abu Dhabi University. Her research interests encompass integrability and exact solutions of differential equations, particularly those modeling nonlinear physical phenomena, including soliton scattering. She developed a highly efficient numerical code based on power expansion for solving nonlinear differential equations. In 2023, Laila obtained a patent on focusing light using acoustic field.
Usama Al Khawaja is a Professor of Physics at the University of Jordan. His main research interests are integrability and exact solutions, nonlinear and quantum optics, quantum computation, and Bose-Einstein condensation. His main achievements in integrability and exact solutions include developing a systematic search method of finding Lax pairs of a given nonlinear partial differential equation. He also developed a highly-accurate convergent power series method for solving regular and fractional nonlinear partial differential equations. He authored more than 100 papers and obtained two patents on applying discrete solitons in all-optical operations, and in converging light using acoustic waves.
