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| List of Figures and Tables | ||
| Preface | ||
| Ch. 1 | Introduction and Overview | 1 |
| Ch. 2 | Holomorphic Riemann-Hilbert Problems for Solitons | 13 |
| Ch. 3 | Semiclassical Soliton Ensembles | 23 |
| 3.1 | Formal WKB Formulae for Even, Bell-Shaped, Real-Valued Initial Conditions | 23 |
| 3.2 | Asymptotic Properties of the Discrete WKB Spectrum | 26 |
| 3.3 | The Satsuma-Yajima Semiclassical Soliton Ensemble | 34 |
| Ch. 4 | Asymptotic Analysis of the Inverse Problem | 37 |
| 4.1 | Introducing the Complex Phase | 38 |
| 4.2 | Representation as a Complex Single-Layer Potential. Passing to the Continum Limit. Conditions on the Complex Phase Leading to the Outer Model Problem | 40 |
| 4.3 | Exact Solution of the Outer Model Problem | 51 |
| 4.4 | Inner Approximations | 69 |
| 4.5 | Estimating the Error | 106 |
| Ch. 5 | Direct Construction of the Complex Phase | 121 |
| 5.1 | Postponing the Inequalities. General Considerations | 121 |
| 5.2 | Imposing the Inequalities. Local and Global Continuation Theory | 138 |
| 5.3 | Modulation Equations | 148 |
| 5.4 | Symmetries of the Endpoint Equations | 159 |
| Ch. 6 | The Genus-Zero Ansatz | 163 |
| 6.1 | Location of the Endpoints for General Data | 163 |
| 6.2 | Success of the Ansatz for General Data and Small Time. Rigorous Small-Time Asymptotics for Semiclassical Soliton Ensembles | 164 |
| 6.3 | Larger-Time Analysis for Soliton Ensembles | 175 |
| 6.4 | The Elliptic Modulation Equations and the Particular Solution of Akhmanov, Sukhorukov, and Khokhlov for the Satsuma-Yajima Initial Data | 191 |
| Ch. 7 | The Transition to Genus Two | 195 |
| 7.1 | Matching the Critical G = 0 Ansatz with a Degenerate G = 2 Ansatz | 196 |
| 7.2 | Perturbing the Degenerate G = 2 Ansatz. Opening the Band I[subscript l][superscript +] by Varying x near x[subscript crit] | 200 |
| Ch. 8 | Variational Theory of the Complex Phase | 215 |
| Ch. 9 | Conclusion and Outlook | 223 |
| 9.1 | Generalization for Nonquantum Values of h | 223 |
| 9.2 | Effect of Complex Singularities in p[superscript 0(n) | 224 |
| 9.3 | Uniformity of the Error near t = 0 | 225 |
| 9.4 | Errors Incurred by Modifying the Initial Data | 225 |
| 9.5 | Analysis of the Max-Min Variational Problem | 226 |
| 9.6 | Initial Data with S(x) [is not equal to] 0 | 227 |
| 9.7 | Final Remarks | 228 |
| App. A | Holder Theory of Local Riemann-Hilbert Problems | 229 |
| App. B | Near-Identity Riemann-Hilbert Problems in L[superscript 2] | 253 |
| Bibliography | 255 | |
| Index | 259 |
| Price | Condition | Delivery | Seller | Action |
| $99.99 | Digital |
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Richard Lewis
reviewed Semiclassical Soliton Ensembles for the Focusing Nonlinear Schrodinger Equation (AM-154) on December 28, 2009
Semiclassical Soliton Ensembles for the Focusing Nonlinear Schrodinger Equation
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Add Semiclassical Soliton Ensembles for the Focusing Nonlinear Schrodinger Equation (AM-154), This book represents the first asymptotic analysis, via completely integrable techniques, of the initial value problem for the focusing nonlinear Schrödinger equation in the semiclassical asymptotic regime. This problem is a key model in nonlinear optical, Semiclassical Soliton Ensembles for the Focusing Nonlinear Schrodinger Equation (AM-154) to the inventory that you are selling on WonderClubX
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Add Semiclassical Soliton Ensembles for the Focusing Nonlinear Schrodinger Equation (AM-154), This book represents the first asymptotic analysis, via completely integrable techniques, of the initial value problem for the focusing nonlinear Schrödinger equation in the semiclassical asymptotic regime. This problem is a key model in nonlinear optical, Semiclassical Soliton Ensembles for the Focusing Nonlinear Schrodinger Equation (AM-154) to your collection on WonderClub |