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Semiclassical soliton ensembles for the focusing nonlinear Schrodinger equation [[electronic resource] /] / Spyridon Kamvissis, Kenneth D.T-R McLaughlin, Peter D. Miller
| Semiclassical soliton ensembles for the focusing nonlinear Schrodinger equation [[electronic resource] /] / Spyridon Kamvissis, Kenneth D.T-R McLaughlin, Peter D. Miller |
| Autore | Kamvissis Spyridon |
| Edizione | [Course Book] |
| Pubbl/distr/stampa | Princeton, NJ, : Princeton University Press, c2003 |
| Descrizione fisica | 1 online resource (280 p.) |
| Disciplina | 530.12/4 |
| Altri autori (Persone) |
McLaughlinK. T-R <1969-> (Kenneth T-R)
MillerPeter D <1967-> (Peter David) |
| Collana | Annals of mathematics studies |
| Soggetto topico |
Schrodinger equation
Wave mechanics |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-299-44345-1
1-4008-3718-9 |
| Classificazione | SI 830 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Frontmatter -- Contents -- Figures and Tables -- Preface -- Chapter 1. Introduction and Overview -- Chapter 2. Holomorphic Riemann-Hilbert Problems for Solitons -- Chapter 3. Semiclassical Soliton Ensembles -- Chapter 4. Asymptotic Analysis of the Inverse Problem -- Chapter 5. Direct Construction of the Complex Phase -- Chapter 6. The Genus - Zero Ansatz -- Chapter 7. The Transition to Genus Two -- Chapter 8. Variational Theory of the Complex Phase -- Chapter 9. Conclusion and Outlook -- Appendix A. H¨older Theory of Local Riemann-Hilbert Problems -- Appendix B. Near-Identity Riemann-Hilbert Problems in L2 -- Bibliography -- Index |
| Record Nr. | UNINA-9910465228803321 |
Kamvissis Spyridon
|
||
| Princeton, NJ, : Princeton University Press, c2003 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Semiclassical soliton ensembles for the focusing nonlinear Schrodinger equation [[electronic resource] /] / Spyridon Kamvissis, Kenneth D.T-R McLaughlin, Peter D. Miller
| Semiclassical soliton ensembles for the focusing nonlinear Schrodinger equation [[electronic resource] /] / Spyridon Kamvissis, Kenneth D.T-R McLaughlin, Peter D. Miller |
| Autore | Kamvissis Spyridon |
| Edizione | [Course Book] |
| Pubbl/distr/stampa | Princeton, NJ, : Princeton University Press, c2003 |
| Descrizione fisica | 1 online resource (280 p.) |
| Disciplina | 530.12/4 |
| Altri autori (Persone) |
McLaughlinK. T-R <1969-> (Kenneth T-R)
MillerPeter D <1967-> (Peter David) |
| Collana | Annals of mathematics studies |
| Soggetto topico |
Schrodinger equation
Wave mechanics |
| Soggetto non controllato |
Abelian integral
Analytic continuation Analytic function Ansatz Approximation Asymptote Asymptotic analysis Asymptotic distribution Asymptotic expansion Banach algebra Basis (linear algebra) Boundary (topology) Boundary value problem Bounded operator Calculation Cauchy's integral formula Cauchy's integral theorem Cauchy's theorem (geometry) Cauchy–Riemann equations Change of variables Coefficient Complex plane Cramer's rule Degeneracy (mathematics) Derivative Diagram (category theory) Differentiable function Differential equation Differential operator Dirac equation Disjoint union Divisor Eigenfunction Eigenvalues and eigenvectors Elliptic integral Energy minimization Equation Euler's formula Euler–Lagrange equation Existential quantification Explicit formulae (L-function) Fourier transform Fredholm theory Function (mathematics) Gauge theory Heteroclinic orbit Hilbert transform Identity matrix Implicit function theorem Implicit function Infimum and supremum Initial value problem Integrable system Integral curve Integral equation Inverse problem Jacobian matrix and determinant Kerr effect Laurent series Limit point Line (geometry) Linear equation Linear space (geometry) Logarithmic derivative Lp space Minor (linear algebra) Monotonic function Neumann series Normalization property (abstract rewriting) Numerical integration Ordinary differential equation Orthogonal polynomials Parameter Parametrix Paraxial approximation Parity (mathematics) Partial derivative Partial differential equation Perturbation theory (quantum mechanics) Perturbation theory Pole (complex analysis) Polynomial Probability measure Quadratic differential Quadratic programming Radon–Nikodym theorem Reflection coefficient Riemann surface Simultaneous equations Sobolev space Soliton Special case Taylor series Theorem Theory Trace (linear algebra) Upper half-plane Variational method (quantum mechanics) Variational principle WKB approximation |
| ISBN |
1-299-44345-1
1-4008-3718-9 |
| Classificazione | SI 830 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Frontmatter -- Contents -- Figures and Tables -- Preface -- Chapter 1. Introduction and Overview -- Chapter 2. Holomorphic Riemann-Hilbert Problems for Solitons -- Chapter 3. Semiclassical Soliton Ensembles -- Chapter 4. Asymptotic Analysis of the Inverse Problem -- Chapter 5. Direct Construction of the Complex Phase -- Chapter 6. The Genus - Zero Ansatz -- Chapter 7. The Transition to Genus Two -- Chapter 8. Variational Theory of the Complex Phase -- Chapter 9. Conclusion and Outlook -- Appendix A. H¨older Theory of Local Riemann-Hilbert Problems -- Appendix B. Near-Identity Riemann-Hilbert Problems in L2 -- Bibliography -- Index |
| Record Nr. | UNINA-9910791959003321 |
|
Kamvissis Spyridon
|
||
| Princeton, NJ, : Princeton University Press, c2003 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Semiclassical soliton ensembles for the focusing nonlinear Schrodinger equation [[electronic resource] /] / Spyridon Kamvissis, Kenneth D.T-R McLaughlin, Peter D. Miller
| Semiclassical soliton ensembles for the focusing nonlinear Schrodinger equation [[electronic resource] /] / Spyridon Kamvissis, Kenneth D.T-R McLaughlin, Peter D. Miller |
| Autore | Kamvissis Spyridon |
| Edizione | [Course Book] |
| Pubbl/distr/stampa | Princeton, NJ, : Princeton University Press, c2003 |
| Descrizione fisica | 1 online resource (280 p.) |
| Disciplina | 530.12/4 |
| Altri autori (Persone) |
McLaughlinK. T-R <1969-> (Kenneth T-R)
MillerPeter D <1967-> (Peter David) |
| Collana | Annals of mathematics studies |
| Soggetto topico |
Schrodinger equation
Wave mechanics |
| Soggetto non controllato |
Abelian integral
Analytic continuation Analytic function Ansatz Approximation Asymptote Asymptotic analysis Asymptotic distribution Asymptotic expansion Banach algebra Basis (linear algebra) Boundary (topology) Boundary value problem Bounded operator Calculation Cauchy's integral formula Cauchy's integral theorem Cauchy's theorem (geometry) Cauchy–Riemann equations Change of variables Coefficient Complex plane Cramer's rule Degeneracy (mathematics) Derivative Diagram (category theory) Differentiable function Differential equation Differential operator Dirac equation Disjoint union Divisor Eigenfunction Eigenvalues and eigenvectors Elliptic integral Energy minimization Equation Euler's formula Euler–Lagrange equation Existential quantification Explicit formulae (L-function) Fourier transform Fredholm theory Function (mathematics) Gauge theory Heteroclinic orbit Hilbert transform Identity matrix Implicit function theorem Implicit function Infimum and supremum Initial value problem Integrable system Integral curve Integral equation Inverse problem Jacobian matrix and determinant Kerr effect Laurent series Limit point Line (geometry) Linear equation Linear space (geometry) Logarithmic derivative Lp space Minor (linear algebra) Monotonic function Neumann series Normalization property (abstract rewriting) Numerical integration Ordinary differential equation Orthogonal polynomials Parameter Parametrix Paraxial approximation Parity (mathematics) Partial derivative Partial differential equation Perturbation theory (quantum mechanics) Perturbation theory Pole (complex analysis) Polynomial Probability measure Quadratic differential Quadratic programming Radon–Nikodym theorem Reflection coefficient Riemann surface Simultaneous equations Sobolev space Soliton Special case Taylor series Theorem Theory Trace (linear algebra) Upper half-plane Variational method (quantum mechanics) Variational principle WKB approximation |
| ISBN |
1-299-44345-1
1-4008-3718-9 |
| Classificazione | SI 830 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Frontmatter -- Contents -- Figures and Tables -- Preface -- Chapter 1. Introduction and Overview -- Chapter 2. Holomorphic Riemann-Hilbert Problems for Solitons -- Chapter 3. Semiclassical Soliton Ensembles -- Chapter 4. Asymptotic Analysis of the Inverse Problem -- Chapter 5. Direct Construction of the Complex Phase -- Chapter 6. The Genus - Zero Ansatz -- Chapter 7. The Transition to Genus Two -- Chapter 8. Variational Theory of the Complex Phase -- Chapter 9. Conclusion and Outlook -- Appendix A. H¨older Theory of Local Riemann-Hilbert Problems -- Appendix B. Near-Identity Riemann-Hilbert Problems in L2 -- Bibliography -- Index |
| Record Nr. | UNINA-9910822848003321 |
|
Kamvissis Spyridon
|
||
| Princeton, NJ, : Princeton University Press, c2003 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The Sine-Gordon equation in the semiclassical limit : dynamics of fluxon condensates / / Robert J. Buckingham, Peter D. Miller
| The Sine-Gordon equation in the semiclassical limit : dynamics of fluxon condensates / / Robert J. Buckingham, Peter D. Miller |
| Autore | Buckingham Robert J. <1979-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2013 |
| Descrizione fisica | 1 online resource (148 p.) |
| Disciplina | 515/.353 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Differential equations, Partial - Asymptotic theory
Riemann-Hilbert problems |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-1059-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Chapter 1. Introduction""; ""1.1. Pure impulse initial data for the sine-Gordon equation. Connection to the Zakharov-Shabat scattering problem""; ""1.2. Exact solutions. Impulse threshold for generation of rotational waves""; ""1.3. Statement of results""; ""1.4. Outline of the rest of the Memoir""; ""1.5. Notation and terminology""; ""Chapter 2. Formulation of the Inverse Problem for Fluxon Condensates""; ""Chapter 3. Elementary Transformations of J( )""; ""3.1. Choice of Î?""; ""3.2. Interpolation of residues. Removal of poles""
""3.3. Analysis of the jump conditions for M( )""""3.4. Control of exponentials. The so-called -function""; ""Chapter 4. Construction of ( )""; ""4.1. Two types of “genus-1� ansatz for ( )""; ""4.2. Finding when =0""; ""4.3. Continuation of to nonzero ""; ""4.4. Solution of the Whitham modulation equations""; ""Chapter 5. Use of ( )""; ""5.1. Opening a lens""; ""5.2. Construction of a global parametrix""; ""5.3. Accuracy of the parametrix. Estimation of the error""; ""Appendix A. Proofs of Propositions Concerning Initial Data""; ""A.1. Proof of Proposition 1.1"" ""A.2. Proof of Proposition 1.2""""Appendix B. Details of the Outer Parametrix in Cases and ""; ""B.1. The outer parametrix in case . Proof of Proposition 5.2 in this case""; ""B.2. The outer parametrix in case . Proof of Proposition 5.2 in this case""; ""B.3. Recovery of the potentials. Proof of Proposition 5.3""; ""Bibliography"" |
| Record Nr. | UNINA-9910480533303321 |
|
Buckingham Robert J. <1979->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The Sine-Gordon equation in the semiclassical limit : dynamics of fluxon condensates / / Robert J. Buckingham, Peter D. Miller
| The Sine-Gordon equation in the semiclassical limit : dynamics of fluxon condensates / / Robert J. Buckingham, Peter D. Miller |
| Autore | Buckingham Robert J. <1979-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2013 |
| Descrizione fisica | 1 online resource (148 p.) |
| Disciplina | 515/.353 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Differential equations, Partial - Asymptotic theory
Riemann-Hilbert problems |
| ISBN | 1-4704-1059-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Chapter 1. Introduction""; ""1.1. Pure impulse initial data for the sine-Gordon equation. Connection to the Zakharov-Shabat scattering problem""; ""1.2. Exact solutions. Impulse threshold for generation of rotational waves""; ""1.3. Statement of results""; ""1.4. Outline of the rest of the Memoir""; ""1.5. Notation and terminology""; ""Chapter 2. Formulation of the Inverse Problem for Fluxon Condensates""; ""Chapter 3. Elementary Transformations of J( )""; ""3.1. Choice of Î?""; ""3.2. Interpolation of residues. Removal of poles""
""3.3. Analysis of the jump conditions for M( )""""3.4. Control of exponentials. The so-called -function""; ""Chapter 4. Construction of ( )""; ""4.1. Two types of “genus-1� ansatz for ( )""; ""4.2. Finding when =0""; ""4.3. Continuation of to nonzero ""; ""4.4. Solution of the Whitham modulation equations""; ""Chapter 5. Use of ( )""; ""5.1. Opening a lens""; ""5.2. Construction of a global parametrix""; ""5.3. Accuracy of the parametrix. Estimation of the error""; ""Appendix A. Proofs of Propositions Concerning Initial Data""; ""A.1. Proof of Proposition 1.1"" ""A.2. Proof of Proposition 1.2""""Appendix B. Details of the Outer Parametrix in Cases and ""; ""B.1. The outer parametrix in case . Proof of Proposition 5.2 in this case""; ""B.2. The outer parametrix in case . Proof of Proposition 5.2 in this case""; ""B.3. Recovery of the potentials. Proof of Proposition 5.3""; ""Bibliography"" |
| Record Nr. | UNINA-9910796037703321 |
|
Buckingham Robert J. <1979->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The Sine-Gordon equation in the semiclassical limit : dynamics of fluxon condensates / / Robert J. Buckingham, Peter D. Miller
| The Sine-Gordon equation in the semiclassical limit : dynamics of fluxon condensates / / Robert J. Buckingham, Peter D. Miller |
| Autore | Buckingham Robert J. <1979-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2013 |
| Descrizione fisica | 1 online resource (148 p.) |
| Disciplina | 515/.353 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Differential equations, Partial - Asymptotic theory
Riemann-Hilbert problems |
| ISBN | 1-4704-1059-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Chapter 1. Introduction""; ""1.1. Pure impulse initial data for the sine-Gordon equation. Connection to the Zakharov-Shabat scattering problem""; ""1.2. Exact solutions. Impulse threshold for generation of rotational waves""; ""1.3. Statement of results""; ""1.4. Outline of the rest of the Memoir""; ""1.5. Notation and terminology""; ""Chapter 2. Formulation of the Inverse Problem for Fluxon Condensates""; ""Chapter 3. Elementary Transformations of J( )""; ""3.1. Choice of Î?""; ""3.2. Interpolation of residues. Removal of poles""
""3.3. Analysis of the jump conditions for M( )""""3.4. Control of exponentials. The so-called -function""; ""Chapter 4. Construction of ( )""; ""4.1. Two types of “genus-1� ansatz for ( )""; ""4.2. Finding when =0""; ""4.3. Continuation of to nonzero ""; ""4.4. Solution of the Whitham modulation equations""; ""Chapter 5. Use of ( )""; ""5.1. Opening a lens""; ""5.2. Construction of a global parametrix""; ""5.3. Accuracy of the parametrix. Estimation of the error""; ""Appendix A. Proofs of Propositions Concerning Initial Data""; ""A.1. Proof of Proposition 1.1"" ""A.2. Proof of Proposition 1.2""""Appendix B. Details of the Outer Parametrix in Cases and ""; ""B.1. The outer parametrix in case . Proof of Proposition 5.2 in this case""; ""B.2. The outer parametrix in case . Proof of Proposition 5.2 in this case""; ""B.3. Recovery of the potentials. Proof of Proposition 5.3""; ""Bibliography"" |
| Record Nr. | UNINA-9910817220803321 |
|
Buckingham Robert J. <1979->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||