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Applications of Analytic and Geometric Methods to Nonlinear Differential Equations
Overview of attention for book
Table of Contents
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Book Overview
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Chapter 1
SDYM Hierarchies and Classical Soliton Systems
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Chapter 2
Twistor Theory, Self-Duality and Integrability
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Chapter 3
Twistor Theory and the Schlesinger Equations
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Chapter 4
Soliton Equations and Connections with Self-Dual Curvature
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Chapter 5
Smooth Static Solutions of the Einstein/Yang-Mills Equations
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Chapter 6
Extended Structures in (2 + 1) Dimensions
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Chapter 7
Null Reductions of the Yang-Mills Self-Duality Equations and Integrable Models in (2 + l)-Dimensions
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Chapter 8
Continuous and Discrete SDYM, and Reductions
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Chapter 9
Rapidly Forced Burgers Equation
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Chapter 10
Nonlinear Evolution Equations from an Inverse Spectral Problem
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Chapter 11
Universal Integrable Nonlinear PDEs
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Chapter 12
Construction of Reflectionless Potentials with Infinitely Many Discrete Eigenvalues
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Chapter 13
Coupling of Completely Integrable Systems: The Perturbation Bundle
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Chapter 14
The Negative Weight KP Hierarchy
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Chapter 15
The Complete Solution to the Constant Quantum Yang-Baxter Equation in Two Dimensions
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Chapter 16
Stimulated Raman Scattering: An Integrable System Which Blows up in Finite Time
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Chapter 17
Integrabile Quantum Mappings and Quantization Aspects of Integrable Discrete-Time Systems
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Chapter 18
Darboux Transformations in (2 + 1)-Dimensions
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Chapter 19
Darboux Theorems and the KP Hierarchy
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Chapter 20
Localized Soliton Solutions for the Davey-Stewartson I and Davey-Stewartson III Equations
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Chapter 21
On Gasdynamic-Solitonic Connections
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Chapter 22
Integrable Cellular Automata and Integrable Algebraic and Functional Equations
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Chapter 23
Classical Differential Geometry and Integrability of Systems of Hydrodynamic Type
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Chapter 24
On the Elliptic 2 + 1 Toda Equation
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Chapter 25
Canonical Bilinear Systems and Soliton Resonances
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Chapter 26
A Perturbative Extension of the Painlevé Test
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Chapter 27
Exact Solutions to the Complex Ginzburg-Landau Equation from a Linear System
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Chapter 28
Generalised Solutions of the Perturbed KdV Equation for Convecting Fluids
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Chapter 29
Modified Singular Manifold Expansion: Application to the Boussinesq and Mikhailov-Shabat Systems
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Chapter 30
Discrete Painlevé Equations: Derivation and Properties
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Chapter 31
A Study of the Fourth Painlevé Equation
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Chapter 32
A Local Asymptotic Method of Seeing the Natural Barrier of the Solutions of the Chazy Equation
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Chapter 33
Rational Solutions and Bäcklund Transformations for the Third Painlevé Equation
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Chapter 34
Some Extensions of the Truncation Process in Painlevé Analysis
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Chapter 35
Potential Symmetries and Linearization
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Chapter 36
Nonclassical Symmetry Reductions and Exact Solutions of Nonlinear Reaction-Diffusion Equations
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Chapter 37
Boundary Conditions on Similarity Solutions
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Chapter 38
Symmetry Reductions and Exact Solutions of the Davey-Stewartson System
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Chapter 39
Dimensional Reduction for Equations Involving Discrete and Continuous Variables
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Chapter 40
Symmetry Reductions and Exact Solutions for a Generalised Boussinesq Equation
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Chapter 41
Continuous Symmetries and Painlevé Reduction of the Kac-Van Moerbeke Equation
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Chapter 42
A New Approach to the Search for Analytical Solutions of Second order Autonomous Nonlinear Differential Equations
Overall attention for this book and its chapters
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Mentioned by
syllabi
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Citations
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Book overview
1. SDYM Hierarchies and Classical Soliton Systems
2. Twistor Theory, Self-Duality and Integrability
3. Twistor Theory and the Schlesinger Equations
4. Soliton Equations and Connections with Self-Dual Curvature
5. Smooth Static Solutions of the Einstein/Yang-Mills Equations
6. Extended Structures in (2 + 1) Dimensions
7. Null Reductions of the Yang-Mills Self-Duality Equations and Integrable Models in (2 + l)-Dimensions
8. Continuous and Discrete SDYM, and Reductions
9. Rapidly Forced Burgers Equation
10. Nonlinear Evolution Equations from an Inverse Spectral Problem
11. Universal Integrable Nonlinear PDEs
12. Construction of Reflectionless Potentials with Infinitely Many Discrete Eigenvalues
13. Coupling of Completely Integrable Systems: The Perturbation Bundle
14. The Negative Weight KP Hierarchy
15. The Complete Solution to the Constant Quantum Yang-Baxter Equation in Two Dimensions
16. Stimulated Raman Scattering: An Integrable System Which Blows up in Finite Time
17. Integrabile Quantum Mappings and Quantization Aspects of Integrable Discrete-Time Systems
18. Darboux Transformations in (2 + 1)-Dimensions
19. Darboux Theorems and the KP Hierarchy
20. Localized Soliton Solutions for the Davey-Stewartson I and Davey-Stewartson III Equations
21. On Gasdynamic-Solitonic Connections
22. Integrable Cellular Automata and Integrable Algebraic and Functional Equations
23. Classical Differential Geometry and Integrability of Systems of Hydrodynamic Type
24. On the Elliptic 2 + 1 Toda Equation
25. Canonical Bilinear Systems and Soliton Resonances
26. A Perturbative Extension of the Painlevé Test
27. Exact Solutions to the Complex Ginzburg-Landau Equation from a Linear System
28. Generalised Solutions of the Perturbed KdV Equation for Convecting Fluids
29. Modified Singular Manifold Expansion: Application to the Boussinesq and Mikhailov-Shabat Systems
30. Discrete Painlevé Equations: Derivation and Properties
31. A Study of the Fourth Painlevé Equation
32. A Local Asymptotic Method of Seeing the Natural Barrier of the Solutions of the Chazy Equation
33. Rational Solutions and Bäcklund Transformations for the Third Painlevé Equation
34. Some Extensions of the Truncation Process in Painlevé Analysis
35. Potential Symmetries and Linearization
36. Nonclassical Symmetry Reductions and Exact Solutions of Nonlinear Reaction-Diffusion Equations
37. Boundary Conditions on Similarity Solutions
38. Symmetry Reductions and Exact Solutions of the Davey-Stewartson System
39. Dimensional Reduction for Equations Involving Discrete and Continuous Variables
40. Symmetry Reductions and Exact Solutions for a Generalised Boussinesq Equation
41. Continuous Symmetries and Painlevé Reduction of the Kac-Van Moerbeke Equation
42. A New Approach to the Search for Analytical Solutions of Second order Autonomous Nonlinear Differential Equations
Summary
Syllabi
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