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Umfang: 1 Online-Ressource (getrennte Seitenzählung) , Illustrationen, Diagramme

Ausgabe: Version: 20191101

ISBN: 9780750324281 , 9780750324274

Serie: IOP ebooks. [2020 collection]

Inhalt: This book collects all known solutions to the nonlinear Schrèodinger equation (NLSE) in one resource. In addition, the book organizes the solutions by classifying and grouping them based on aspects and symmetries they possess. Although most of the solutions presented in this book have been derived elsewhere using various methods, the authors present a systematic derivation of many solutions and even include new derivations. They have also presented symmetries and reductions that connect different solutions through transformations and enable classifying new solutions into known classes. For the user to verify that the presented solutions do satisfy the NLSE, this monumental work is accompanied by Mathematica Notebooks containing all solutions. This work also features a large number of figures, and animations are included to help visualize solutions and their dynamics.

Anmerkung: "Version: 20191101"--Title page verso. - Includes bibliographical references. - Title from PDF title page (viewed on December 9, 2019)

Weitere Ausg.: ISBN 9780750324267

Weitere Ausg.: Erscheint auch als Druck-Ausgabe Al Khawaja, Usama, 1970 - Handbook of exact solutions to the nonlinear Schrödinger equations Bristol : IOP Publishing, 2020 ISBN 9780750324267

Weitere Ausg.: ISBN 0750324260

Sprache: Englisch

Fachgebiete: Physik

DOI: 10.1088/978-0-7503-2428-1

URL: Volltext

URL: lizenzpflichtig

UID:

Umfang: 1 online resource (396 pages)

Ausgabe: 1st ed.

ISBN: 9780750324281

Serie: IOP Ebooks Series

Inhalt: This book collects all known solutions to the in one resource nonlinear Schrödinger equation. In addition, the book organizes the solutions by classifying and grouping them based on aspects and symmetries they possess. Accompanied by Mathematica notebooks containing all solutions, it also features a large number of figures, and animations to help readers to visualize solutions and their dynamics.

Anmerkung: Intro -- Preface -- Acknowledgments -- Author Biographies -- Usama Al Khawaja -- Laila Al Sakkaf -- Notation -- Chapter 1 Introduction -- References -- Chapter 2 Fundamental Nonlinear Schrödinger Equation -- A Glance at Chapter 2 -- A Statistical View of Chapter 2 -- 2.1 NLSE with Cubic Nonlinearity -- 2.1.1 Real Dispersion and Nonlinearity Coefficients -- 2.2 Summary of Subsection 2.1.1 -- 2.2.1 Complex Dispersion and Nonlinearity Coefficients -- 2.3 Summary of Subsection 2.2.1 -- References -- Chapter 3 Nonlinear Schrödinger Equation with Power Law and Dual Power Law Nonlinearities -- A Glance at Chapter 3 -- A Statistical View of Chapter 3 -- 3.1 NLSE with Power Law Nonlinearity -- 3.1.1 Reduction to the Fundamental NLSE -- 3.2 Summary of Section 3.1 -- 3.3 NLSE with Dual Power Law Nonlinearity -- 3.4 Summary of Section 3.3 -- References -- Chapter 4 Nonlinear Schrödinger Equation with Higher Order Terms -- A Glance at Chapter 4 -- A Statistical View of Chapter 4 -- 4.1 NLSE with Third Order Dispersion, Self-Steepening, and Self-Frequency Shift -- 4.2 Summary of Section 4.1 -- 4.3 Special Cases of Equation (4.1) -- 4.3.1 Case I: Hirota Equation (HE) -- 4.3.2 Case II: Sasa-Satsuma Equation (SSE) -- 4.4 NLSE with First and Third Order Dispersions, Self-Steepening, Self-Frequency Shift, and Potential -- 4.5 Summary of Section 4.4 -- 4.6 NLSE with Fourth Order Dispersion -- 4.7 Summary of Section 4.6 -- 4.8 NLSE with Fourth Order Dispersion and Power Law Nonlinearity -- 4.9 Summary of Section 4.8 -- 4.10 NLSE with Third and Fourth Order Dispersions and Cubic and Quintic Nonlinearities -- 4.11 Summary of Section 4.10 -- 4.12 NLSE with Third and Fourth Order Dispersions, Self-Steepening, Self-Frequency Shift, and Cubic and Quintic Nonlinearities -- 4.13 Summary of Section 4.12 -- 4.14 NLSE with ∣ψτ̔̈“““”·2-Dependent Dispersion. , 4.15 Infinite Hierarchy of Integrable NLSEs with Higher Order Terms -- 4.15.1 Constant Coefficients -- 4.15.2 Function Coefficients -- 4.16 Summary of Section 4.15 -- References -- Chapter 5 Scaling Transformations -- A Glance at Chapter 5 -- A Statistical View of Chapter 5 -- 5.1 Fundamental NLSE to Fundamental NLSE with Different Constant Coefficients -- 5.2 Defocusing (Focusing) NLSE to Focusing (Defocusing) NLSE -- 5.3 Galilean Transformation (Movable Solutions) -- 5.4 Function Coefficients -- 5.4.1 Constant Dispersion and Complex Potential -- 5.4.2 Constant Dispersion and Real Quadratic Potential -- 5.4.3 Constant Dispersion and Real Linear Potential -- 5.4.4 Constant Nonlinearity and Complex Potential -- 5.4.5 Constant Nonlinearity and Real Quadratic Potential -- 5.4.6 Constant Nonlinearity and Real Linear Potential -- 5.5 Solution-Dependent Transformation -- 5.5.1 Special Case I: Stationary Solution, Constant Dispersion and Nonlinearity Coefficients -- 5.5.2 Special Case II: PT-Symmetric Potential -- 5.5.3 Special Case III: Stationary Solution, Constant Dispersion and Nonlinearity Coefficients, and Real Potential -- 5.6 Summary of Sections 5.1-5.5 -- 5.7 Other Equations: NLSE with Periodic Potentials -- 5.7.1 General Case: sn2(x,m) Potential -- 5.7.2 Specific Case: sin2(x) Potential -- 5.8 Summary of Section 5.7 -- Reference -- Chapter 6 Nonlinear Schrödinger Equation in (N + 1)-Dimensions -- A Glance at Chapter 6 -- A Statistical View of Chapter 6 -- 6.1 (N + 1)-Dimensional NLSE with Cubic Nonlinearity -- 6.2 (N + 1)-Dimensional NLSE with Power Law Nonlinearity -- 6.3 (N + 1)-Dimensional NLSE with Dual Power Law Nonlinearity -- 6.4 Galilean Transformation in (N + 1)-Dimensions (Movable Solutions) -- 6.5 NLSE in (2 + 1)-Dimensions with Φx1x2 Term -- 6.6 Summary of Sections 6.1-6.5. , 6.7 (N + 1)-Dimensional Isotropic NLSE with Cubic Nonlinearity in Polar Coordinate System -- 6.7.1 Angular Dependence -- 6.7.2 Constant Dispersion and Real Potential -- 6.8 Summary of Section 6.7 -- 6.9 Power Series Solutions to (2 + 1)-Dimensional NLSE with Cubic Nonlinearity in a Polar Coordinate System -- 6.9.1 Family of Infinite Number of Localized Solutions -- References -- Chapter 7 Coupled Nonlinear Schrödinger Equations -- A Glance at Chapter 7 -- A Statistical View of Chapter 7 -- 7.1 Fundamental Coupled NLSE Manakov System -- 7.2 Summary of Section 7.1 -- 7.3 Symmetry Reductions -- 7.3.1 Symmetry Reduction I -- 7.3.2 Symmetry Reduction II -- 7.3.3 Symmetry Reduction III -- 7.3.4 Symmetry Reduction IV -- 7.3.5 Symmetry Reduction V -- 7.4 Scaling Transformations -- 7.4.1 Linear and Nonlinear Coupling -- 7.4.2 Complex Coupling -- 7.4.3 Function Coefficients -- 7.5 Summary of Sections 7.3-7.4 -- 7.6 (N + 1)-Dimensional Coupled NLSE -- 7.6.1 Reduction to 1D Manakov System -- 7.7 Symmetry Reductions of (N + 1)-Dimensional CNLSE to Scalar NLSE -- 7.7.1 Symmetry Reduction I -- 7.7.2 Symmetry Reduction II -- 7.7.3 Symmetry Reduction III -- 7.8 (N + 1)-Dimensional Scaling Transformations -- 7.8.1 Linear and Nonlinear Coupling -- 7.8.2 Complex Coupling -- 7.9 Summary of Sections 7.7-7.8 -- References -- Chapter 8 Discrete Nonlinear Schrödinger Equation -- A Glance at Chapter 8 -- A Statistical View of Chapter 8 -- 8.1 Discrete NLSE with Saturable Nonlinearity -- 8.1.1 Nonstaggered Solutions -- 8.1.2 Staggered Solutions -- 8.2 Summary of Section 8.1 -- 8.3 Short-period Solutions with General, Kerr, and Saturable Nonlinearities -- 8.4 Ablowitz-Ladik Equation -- 8.5 Summary of Section 8.4 -- 8.6 Cubic-quintic Discrete NLSE -- 8.7 Summary of Section 8.6 -- 8.8 Generalized Discrete NLSE -- 8.9 Summary of Section 8.8 -- 8.10 Coupled Salerno Equations. , 8.11 Summary of Section 8.10 -- 8.12 Coupled Ablowitz-Ladik Equation -- 8.13 Summary of Section 8.12 -- 8.14 Coupled Saturable Discrete NLSE -- 8.15 Summary of Section 8.14 -- References -- Chapter 9 Nonlocal Nonlinear Schrödinger Equation -- A Glance at Chapter 9 -- A Statistical View of Chapter 9 -- 9.1 Nonlocal NLSE -- 9.2 Nonlocal Coupled NLSE -- 9.3 Symmetry Reductions to Scalar Nonlocal NLSE -- 9.3.1 Symmetry Reduction I -- 9.3.2 Symmetry Reduction II -- 9.3.3 Symmetry Reduction III -- 9.4 Scaling Transformations -- 9.4.1 Linear and Nonlinear Coupling -- 9.4.2 Complex Coupling -- 9.5 Nonlocal Discrete NLSE with Saturable Nonlinearity -- 9.5.1 Nonstaggered Solutions -- 9.5.2 Staggered Solutions -- 9.6 Nonlocal Ablowitz-Ladik Equation -- 9.7 Nonlocal Cubic-Quintic Discrete NLSE -- 9.8 Summary of Chapter 9 -- Chapter -- A.1 Derivation of Some Solutions of Section 2.1 -- A.1.1 Schematic Representation -- A.1.2 Detailed Derivations -- A.2 Derivation of Some Solutions of Section 3.1 -- A.2.1 Schematic Representation -- A.2.2 Detailed Derivations -- A.3 Derivation of Some Solutions of Section 3.3 -- A.3.1 Schematic Representation -- A.3.2 Detailed Derivations -- Chapter -- B.1 Darboux Transformation -- Link between NLSE and LP -- Seed Solution -- Darboux Transformation -- Symmetry Reduction -- B.1.1 Bright Soliton Solution: Zero Seed -- B.1.2 Generalized Breather Solution for Focusing and Defocusing Nonlinearity: CW Seed -- Chapter -- C.1 Function Coefficients -- C.2 Solution-Dependent Transformation -- C.3 Similarity Transformation for the NLSE in (N + 1)-Dimensions.

Weitere Ausg.: Print version: Al Khawaja, Usama Handbook of Exact Solutions to the Nonlinear Schrödinger Equations Bristol : Institute of Physics Publishing,c2019 ISBN 9780750324298

Sprache: Englisch

Schlagwort(e): Electronic books.

URL: Click to View

UID:

Umfang: 1 online resource (various pagings) : , illustrations (some color).

ISBN: 9780750324281 , 9780750324274

Serie: IOP ebooks. [2020 collection]

Inhalt: This book collects all known solutions to the nonlinear Schrödinger equation (NLSE) in one resource. In addition, the book organizes the solutions by classifying and grouping them based on aspects and symmetries they possess. Although most of the solutions presented in this book have been derived elsewhere using various methods, the authors present a systematic derivation of many solutions and even include new derivations. They have also presented symmetries and reductions that connect different solutions through transformations and enable classifying new solutions into known classes. For the user to verify that the presented solutions do satisfy the NLSE, this monumental work is accompanied by Mathematica Notebooks containing all solutions. This work also features a large number of figures, and animations are included to help visualize solutions and their dynamics.

Anmerkung: "Version: 20191101"--Title page verso. , 1. Introduction -- 2. Fundamental nonlinear Schrödinger equation -- 2.1. NLSE with cubic nonlinearity -- 2.2. Summary of subsection 2.1.1 -- 2.3. Summary of subsection 2.2.1 , 3. Nonlinear Schrödinger equation with power law and dual power law nonlinearities -- 3.1. NLSE with power law nonlinearity -- 3.2. Summary of section 3.1 -- 3.3. NLSE with Dual power law nonlinearity -- 3.4. Summary of section 3.3 , 4. Nonlinear Schrödinger equation with higher order terms -- 4.1. NLSE with third order dispersion, self-steepening, and self-frequency shift -- 4.2. Summary of section 4.1 -- 4.3. Special cases of equation (4.1) -- 4.4. NLSE with first and third order dispersions, self-steepening, self-frequency shift, and potential -- 4.5. Summary of section 4.4 -- 4.6. NLSE with fourth order dispersion -- 4.7. Summary of section 4.6 -- 4.8. NLSE with fourth order dispersion and power law nonlinearity -- 4.9. Summary of section 4.8 -- 4.10. NLSE with third and fourth order dispersions and cubic and quintic nonlinearities -- 4.11. Summary of section 4.10 -- 4.12. NLSE with third and fourth order dispersions, self-steepening, self-frequency shift, and cubic and quintic nonlinearities -- 4.13. Summary of section 4.12 -- 4.14. NLSE with [pipe][psi][pipe]2-dependent dispersion -- 4.15. Infinite hierarchy of integrable NLSEs with higher order terms -- 4.16. Summary of section 4.15 , 5. Scaling transformations -- 5.1. Fundamental NLSE to fundamental NLSE with different constant coefficients -- 5.2. Defocusing (focusing) NLSE to focusing (defocusing) NLSE -- 5.3. Galilean transformation (movable solutions) -- 5.4. Function coefficients -- 5.5. Solution-dependent transformation -- 5.6. Summary of sections 5.1-5.5 -- 5.7. Other equations : NLSE with periodic potentials -- 5.8. Summary of section 5.7 , 6. Nonlinear Schrödinger equation in (N + 1)-dimensions -- 6.1. (N + 1)-dimensional NLSE with cubic nonlinearity -- 6.2. (N + 1)-dimensional NLSE with power law nonlinearity -- 6.3. (N + 1)-dimensional NLSE with dual power law nonlinearity -- 6.4. Galilean Transformation in (N + 1)-dimensions (movable solutions) -- 6.5. NLSE in (2 + 1)-Dimensions with [phi]x1x2 term -- 6.6. Summary of sections 6.1-6.5 -- 6.7. (N + 1)-dimensional isotropic NLSE with cubic nonlinearity in polar coordinate system -- 6.8. Summary of section 6.7 -- 6.9. Power series solutions to (2 + 1)-dimensional NLSE with cubic nonlinearity in a polar coordinate system , 7. Coupled nonlinear Schrödinger equations -- 7.1. Fundamental coupled NLSE Manakov system -- 7.2. Summary of section 7.1 -- 7.3. Symmetry reductions -- 7.4. Scaling transformations -- 7.5. Summary of sections 7.3-7.4 -- 7.6. (N + 1)-Dimensional coupled NLSE (N + 1)-dimensional Manakov system -- 7.7. Symmetry reductions of (N + 1)-dimensional CNLSE to Scalar NLSE -- 7.8. (N + 1)-dimensional scaling transformations -- 7.9. Summary of sections 7.7-7.8 , 8. Discrete nonlinear Schrödinger equation -- 8.1. Discrete NLSE with saturable nonlinearity -- 8.2. Summary of section 8.1 -- 8.3. Short-period solutions with general, Kerr, and saturable nonlinearities -- 8.4. Ablowitz-Ladik equation -- 8.5. Summary of section 8.4 -- 8.6. Cubic-quintic discrete NLSE -- 8.7. Summary of section 8.6 -- 8.8. Generalized discrete NLSE -- 8.9. Summary of section 8.8 -- 8.10. Coupled Salerno equations -- 8.11. Summary of section 8.10 -- 8.12. Coupled Ablowitz-Ladik equation -- 8.13. Summary of section 8.12 -- 8.14. Coupled saturable discrete NLSE -- 8.15. Summary of section 8.14 , 9. Nonlocal nonlinear Schrödinger equation -- 9.1. Nonlocal NLSE -- 9.2. Nonlocal coupled NLSE -- 9.3. Symmetry reductions to scalar nonlocal NLSE -- 9.4. Scaling transformations -- 9.5. Nonlocal discrete NLSE with saturable nonlinearity -- 9.6. Nonlocal Ablowitz-Ladik Equation -- 9.7. Nonlocal cubic-quintic discrete NLSE -- 9.8. Summary of chapter 9 , Appendices. A. Derivation of some solutions of chapters 2 and 3 -- B. Darboux transformation single soliton and breather solutions -- C. Derivation of the similarity transformations in chapter. , Also available in print. , Mode of access: World Wide Web. , System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.

Weitere Ausg.: Print version: ISBN 9780750324267

Sprache: Englisch

DOI: 10.1088/978-0-7503-2428-1

URL: https://iopscience.iop.org/book/978-0-7503-2428-1