Handbook of exact solutions to the nonlinear Schr?odinger equations /

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Handbook of exact solutions to the nonlinear Schr?odinger equations /

Khawaja, Usama Al, - Personal Name; Institute of Physics (Great Britain), - Personal Name; Sakkaf, Laila Al, - Personal Name;

"Version: 20240901"--Title page verso.Includes bibliographical references.1. Introduction -- 2. Fundamental nonlinear Schr?odinger equation -- 2.1. Introduction -- 2.2. NLSE with cubic nonlinearity3. Nonlinear Schr?odinger equation with power law and dual power law nonlinearities -- 3.1. Introduction -- 3.2. NLSE with power law nonlinearity -- 3.3. Summary of section 3.2 -- 3.4. NLSE with dual power law nonlinearity -- 3.5. Summary of section 3.44. Nonlinear Schr?odinger equation with higher order terms -- 4.1. Introduction -- 4.2. NLSE with third order dispersion, self-steepening, and self-frequency shift -- 4.3. Summary of section 4.2 -- 4.4. Special cases of equation (4.17) -- 4.5. NLSE with first and third order dispersions, self-steepening, self-frequency shift, and potential -- 4.6. Summary of section 4.5 -- 4.7. NLSE with t-dependent coefficients and first order dispersion -- 4.8. Summary of section 4.7 -- 4.9. NLSE with fourth order dispersion -- 4.10. Summary of section 4.9 -- 4.11. NLSE with fourth order dispersion and power law nonlinearity -- 4.12. Summary of section 4.11 -- 4.13. NLSE with third and fourth order dispersions and cubic and quintic nonlinearities -- 4.14. Summary of section 4.13 -- 4.15. NLSE with third and fourth order dispersions, self-steepening, self-frequency shift, and cubic and quintic nonlinearities -- 4.16. Summary of section 4.15 -- 4.17. NLSE with y 2 | | -dependent dispersion -- 4.18. Infinite hierarchy of integrable NLSEs with higher order terms -- 4.19. Summary of section 4.185. Scaling transformations -- 5.1. Introduction -- 5.2. Fundamental NLSE to fundamental NLSE with different constant coefficients -- 5.3. Defocusing (focusing) NLSE to focusing (defocusing) NLSE -- 5.4. Galilean transformation (moving solutions) -- 5.5. Function coefficients -- 5.6. Solution-dependent transformation -- 5.7. Summary of sections 5.2-5.6 -- 5.8. Other equations -- 5.9. Summary of section 5.86. Nonlinear Schr?odinger equation in (N + 1)-dimensions -- 6.1. Introduction -- 6.2. (N + 1)-dimensional NLSE with cubic nonlinearity -- 6.3. (N + 1)-dimensional NLSE with power law nonlinearity -- 6.4. (N + 1)-dimensional NLSE with dual power law nonlinearity -- 6.5. Galilean transformation in (N + 1)-dimensions (moving solutions) -- 6.6. NLSE in (2 + 1)-dimensions with [phi]x x1 2 term -- 6.7. Summary of sections 6.2-6.6 -- 6.8. (N + 1)-dimensional isotropic NLSE with cubic nonlinearity in polar coordinate system -- 6.9. Summary of section 6.8 -- 6.10. Power series solutions to (2 + 1)-dimensional NLSE with cubic nonlinearity in polar coordinate system7. Coupled nonlinear Schr?odinger equations -- 7.1. Introduction -- 7.2. Fundamental coupled NLSE Manakov system -- 7.3. Summary of section 7.2 -- 7.4. Symmetry seductions -- 7.5. Scaling transformations -- 7.6. Summary of sections 7.4-7.5 -- 7.7. (N + 1)-dimensional coupled NLSE (N + 1)-dimensional Manakov system -- 7.8. Symmetry reductions of (N + 1)-dimensional cNLSE to scalar NLSE -- 7.9. (N + 1)-dimensional scaling transformations -- 7.10. Composite solutions: nonlinear superposition -- 7.11. Summary of sections 7.8-7.108. Discrete nonlinear Schr?odinger equation -- 8.1. Introduction -- 8.2. Discrete NLSE with saturable nonlinearity -- 8.3. Summary of section 8.2 -- 8.4. Short-period solutions with general, Kerr, and saturable nonlinearities -- 8.5. ABLOWITZ-LADIK equation -- 8.6. Summary of section 8.5 -- 8.7. Cubic-quintic discrete NLSE -- 8.8. Summary of section 8.7 -- 8.9. Generalized discrete NLSE -- 8.10. Summary of section 8.9 -- 8.11. Coupled Salerno equations -- 8.12. Summary of section 8.11 -- 8.13. Coupled Ablowitz-Ladik equation -- 8.14. Summary of section 8.13 -- 8.15. Coupled saturable discrete NLSE -- 8.16. Summary of section 8.159. Nonlocal nonlinear Schr?odinger equation -- 9.1. Introduction -- 9.2. Nonlocal NLSE -- 9.3. Yang's nonlocal NLSE -- 9.4. Nonlocal coupled NLSE -- 9.5. Symmetry reductions to scalar nonlocal NLSE -- 9.6. Scaling transformations -- 9.7. Nonlocal discrete NLSE with saturable nonlinearity -- 9.8. Nonlocal Ablowitz-Ladik equation -- 9.9. Nonlocal cubic-quintic discrete NLSE -- 9.10. Summary of chapter 910. Fractional nonlinear Schr?odinger equation -- 10.1. Introduction -- 10.2. Conformable fractional derivative -- 10.3. Summary of section 10.2 -- 10.4. Fractal fractional derivative -- 10.5. Summary of section 10.4 -- 10.6. Atangana ([beta]) fractional derivative -- 10.7. Summary of section 10.6Appendix A. Derivation of some solutions of chapters 2 and 3 -- Appendix B. Darboux transformation: single soliton and breather solutions -- Appendix C. Derivation of the similarity transformations in chapter 5.Full-text restricted to subscribers or individual document purchasers.Throughout the long history of the nonlinear Schr?odinger equation (NLSE), many exact analytical solutions have been found and they continue to grow as new solutions are being sought and discovered. This book aims to organize the solutions by classifying and grouping them based on aspects and symmetries they possess. The authors present a systematic derivation of many solutions and even include new derivations. This expanded second edition contains new solutions published or derived since the first edition. Noting the increasing interest in and applications of the fractional nonlinear Schr?odinger equation, a new chapter devoted to this topic has been added. Each chapter now also features an introductory section documenting the history, background, and physical systems described by the equations at hand.Professional and scholarly.Also available in print.Mode of access: World Wide Web.System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.Usama Al Khawaja is a theoretical Physicist who is currently a full professor in the Department of Physics at the University of Jordan. He is specialized in solitons and their applications, exact solutions and methods of solution. Laila Al Sakkaf is currently an assistant professor in the College of Engineering at Abu Dhabi University. She is specialized in solitons and their applications, exact solutions and methods of solution.Title from PDF title page (viewed on October 3, 2024).

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Series Title: -
Call Number: -
Publisher: : .,
Collation: 1 online resource (various pagings) :illustrations (some color).
Language: English
ISBN/ISSN: 9780750359542
Classification: 530.124
Content Type: -
Media Type: -
Carrier Type: -
Edition: Second edition.
Subject(s): SCIENCE / Physics / Mathematical & Computational.
Mathematical physics.
Schr?odinger equation.
Differential equations, Nonlinear.
Nonlinear wave equations.
Specific Detail Info: -
Statement of Responsibility: Usama Al Khawaja, Laila Al Sakkaf.

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