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Caustics, Catastrophes and Wave Fields [[electronic resource] /] / by Yu.A. Kravtsov, Yu.I. Orlov
| Caustics, Catastrophes and Wave Fields [[electronic resource] /] / by Yu.A. Kravtsov, Yu.I. Orlov |
| Autore | Kravtsov Yu.A |
| Edizione | [2nd ed. 1993.] |
| Pubbl/distr/stampa | Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1993 |
| Descrizione fisica | 1 online resource (XII, 216 p.) |
| Disciplina | 534 |
| Collana | Springer Series on Wave Phenomena |
| Soggetto topico |
Acoustics
Optics Electrodynamics Classical Electrodynamics |
| ISBN | 3-642-59887-0 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1 Introduction -- 1.1 Caustic Fields in Physical Problems -- 1.2 The Geometrical Aspect of the Caustic Problem -- 1.3 The Wave Aspect of the Caustic Problem -- 2 Rays and Caustics -- 2.1 Equations of Geometrical Optics -- 2.2 The Role of Rays in the Method of Geometrical Optics -- 2.4 Complex Rays -- 3 Caustics as Catastrophes -- 3.1 Mappings Induced by Rays -- 3.2 Classification of Typical Caustics -- 4 Typical Integrals of Catastrophe Theory -- 4.1 Standard Caustic Integrals -- 4.2 The Airy Integral -- 4.3. The Pearcey Integral -- 4.4 Other Typical Integrals -- 5 Uniform Caustic Asymptotics Derived with Standard Integrals -- 5.1 Uniform Airy Asymptotic of a Scalar Field -- 5.2 Uniform Caustic Asymptotics Based on General Standard Integrals -- 5.3 Illustrative Examples -- 6 Maslov’s Method of the Canonical Operator -- 6.1 Principal Relationships -- 6.2 Specific Problems -- 6.3. Generalization by Using Fractional Transformations -- 7 Method of Interference Integrals -- 7.1 Ray Type Integrals -- 7.2 Caustic Integrals -- 7.3 Additional Topics and Generalizations -- 8 Penumbra Caustics -- 8.1 Broken Penumbra Caustics -- 8.2 Penumbra Caustics of Diffraction Rays -- 8.3 Penumbra Caustics and Edge Catastrophes -- 9 Modifications and Generalizations of Standard Integrals and Functions -- 9.1 Nonpolynomial Phase Standard Integrals -- 9.2 Structurally Unstable Caustics -- 9.3 Standard Integrals with Amplitude Correction -- 9.4 Reflection from a Barrier and Oscillations in a Potential Well -- 9.5 Standard Functions Induced by Ordinary Differential Equations -- 10 Caustics Revisited -- 10.1 Caustics in Dispersive Media -- 10.3 Complex Caustics -- 10.4 Random Caustics -- 10.5 Caustics in Quantum Mechanical Problems -- 10.6 Concluding Remarks -- References -- List of Symbols. |
| Record Nr. | UNINA-9910480899803321 |
Kravtsov Yu.A
|
||
| Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1993 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Caustics, Catastrophes and Wave Fields [[electronic resource] /] / by Yu.A. Kravtsov, Yu.I. Orlov
| Caustics, Catastrophes and Wave Fields [[electronic resource] /] / by Yu.A. Kravtsov, Yu.I. Orlov |
| Autore | Kravtsov Yu.A |
| Edizione | [2nd ed. 1993.] |
| Pubbl/distr/stampa | Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1993 |
| Descrizione fisica | 1 online resource (XII, 216 p.) |
| Disciplina | 534 |
| Collana | Springer Series on Wave Phenomena |
| Soggetto topico |
Acoustics
Optics Electrodynamics Classical Electrodynamics |
| ISBN | 3-642-59887-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1 Introduction -- 1.1 Caustic Fields in Physical Problems -- 1.2 The Geometrical Aspect of the Caustic Problem -- 1.3 The Wave Aspect of the Caustic Problem -- 2 Rays and Caustics -- 2.1 Equations of Geometrical Optics -- 2.2 The Role of Rays in the Method of Geometrical Optics -- 2.4 Complex Rays -- 3 Caustics as Catastrophes -- 3.1 Mappings Induced by Rays -- 3.2 Classification of Typical Caustics -- 4 Typical Integrals of Catastrophe Theory -- 4.1 Standard Caustic Integrals -- 4.2 The Airy Integral -- 4.3. The Pearcey Integral -- 4.4 Other Typical Integrals -- 5 Uniform Caustic Asymptotics Derived with Standard Integrals -- 5.1 Uniform Airy Asymptotic of a Scalar Field -- 5.2 Uniform Caustic Asymptotics Based on General Standard Integrals -- 5.3 Illustrative Examples -- 6 Maslov’s Method of the Canonical Operator -- 6.1 Principal Relationships -- 6.2 Specific Problems -- 6.3. Generalization by Using Fractional Transformations -- 7 Method of Interference Integrals -- 7.1 Ray Type Integrals -- 7.2 Caustic Integrals -- 7.3 Additional Topics and Generalizations -- 8 Penumbra Caustics -- 8.1 Broken Penumbra Caustics -- 8.2 Penumbra Caustics of Diffraction Rays -- 8.3 Penumbra Caustics and Edge Catastrophes -- 9 Modifications and Generalizations of Standard Integrals and Functions -- 9.1 Nonpolynomial Phase Standard Integrals -- 9.2 Structurally Unstable Caustics -- 9.3 Standard Integrals with Amplitude Correction -- 9.4 Reflection from a Barrier and Oscillations in a Potential Well -- 9.5 Standard Functions Induced by Ordinary Differential Equations -- 10 Caustics Revisited -- 10.1 Caustics in Dispersive Media -- 10.3 Complex Caustics -- 10.4 Random Caustics -- 10.5 Caustics in Quantum Mechanical Problems -- 10.6 Concluding Remarks -- References -- List of Symbols. |
| Record Nr. | UNINA-9910789214803321 |
|
Kravtsov Yu.A
|
||
| Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1993 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Caustics, Catastrophes and Wave Fields [[electronic resource] /] / by Yu.A. Kravtsov, Yu.I. Orlov
| Caustics, Catastrophes and Wave Fields [[electronic resource] /] / by Yu.A. Kravtsov, Yu.I. Orlov |
| Autore | Kravtsov Yu.A |
| Edizione | [2nd ed. 1993.] |
| Pubbl/distr/stampa | Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1993 |
| Descrizione fisica | 1 online resource (XII, 216 p.) |
| Disciplina | 534 |
| Collana | Springer Series on Wave Phenomena |
| Soggetto topico |
Acoustics
Optics Electrodynamics Classical Electrodynamics |
| ISBN | 3-642-59887-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1 Introduction -- 1.1 Caustic Fields in Physical Problems -- 1.2 The Geometrical Aspect of the Caustic Problem -- 1.3 The Wave Aspect of the Caustic Problem -- 2 Rays and Caustics -- 2.1 Equations of Geometrical Optics -- 2.2 The Role of Rays in the Method of Geometrical Optics -- 2.4 Complex Rays -- 3 Caustics as Catastrophes -- 3.1 Mappings Induced by Rays -- 3.2 Classification of Typical Caustics -- 4 Typical Integrals of Catastrophe Theory -- 4.1 Standard Caustic Integrals -- 4.2 The Airy Integral -- 4.3. The Pearcey Integral -- 4.4 Other Typical Integrals -- 5 Uniform Caustic Asymptotics Derived with Standard Integrals -- 5.1 Uniform Airy Asymptotic of a Scalar Field -- 5.2 Uniform Caustic Asymptotics Based on General Standard Integrals -- 5.3 Illustrative Examples -- 6 Maslov’s Method of the Canonical Operator -- 6.1 Principal Relationships -- 6.2 Specific Problems -- 6.3. Generalization by Using Fractional Transformations -- 7 Method of Interference Integrals -- 7.1 Ray Type Integrals -- 7.2 Caustic Integrals -- 7.3 Additional Topics and Generalizations -- 8 Penumbra Caustics -- 8.1 Broken Penumbra Caustics -- 8.2 Penumbra Caustics of Diffraction Rays -- 8.3 Penumbra Caustics and Edge Catastrophes -- 9 Modifications and Generalizations of Standard Integrals and Functions -- 9.1 Nonpolynomial Phase Standard Integrals -- 9.2 Structurally Unstable Caustics -- 9.3 Standard Integrals with Amplitude Correction -- 9.4 Reflection from a Barrier and Oscillations in a Potential Well -- 9.5 Standard Functions Induced by Ordinary Differential Equations -- 10 Caustics Revisited -- 10.1 Caustics in Dispersive Media -- 10.3 Complex Caustics -- 10.4 Random Caustics -- 10.5 Caustics in Quantum Mechanical Problems -- 10.6 Concluding Remarks -- References -- List of Symbols. |
| Record Nr. | UNINA-9910813105403321 |
|
Kravtsov Yu.A
|
||
| Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1993 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||