A Dressing Method in Mathematical Physics
The monograph is devoted to the systematic presentation of the so called "dressing method" for solving differential equations (both linear and nonlinear) of mathematical physics. The essence of the dressing method consists in a generation of new non-trivial solutions of a given equation fr...
Enregistré dans:
| Auteurs principaux: | , |
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| Format: | Livre numérique |
| Langue: | Anglais |
| Publié: |
Dordrecht :
Springer Netherlands
[20..].
Cham : Springer Nature |
| Édition: | 1st ed. 2007. |
| Collection: | Mathematical Physics Studies
28 |
| Accès en ligne: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Note: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • A dressing method in mathematical physics, by Evgeny V. Doktorov, ... and Sergey B. Leble, ..., Dordrecht, Springer, 2007, 1 vol. (XXIV-383 p.), Mathematical physics studies, 978-1-402-06138-7 • A Dressing Method in Mathematical Physics, Texte imprimé, 9789048113767 • A Dressing Method in Mathematical Physics, Texte imprimé, 9789048175482 • A dressing method in mathematical physics, by Evgeny V. Doktorov, ... and Sergey B. Leble, ..., Dordrecht, Springer, 2007, 1 vol. (XXIV-383 p.), Mathematical physics studies, 978-1-402-06138-7 |
| Résumé: | The monograph is devoted to the systematic presentation of the so called "dressing method" for solving differential equations (both linear and nonlinear) of mathematical physics. The essence of the dressing method consists in a generation of new non-trivial solutions of a given equation from (maybe trivial) solution of the same or related equation. The Moutard and Darboux transformations discovered in XIX century as applied to linear equations, the Bäcklund transformation in differential geometry of surfaces, the factorization method, the Riemann-Hilbert problem in the form proposed by Shabat and Zakharov for soliton equations and its extension in terms of the d-bar formalism comprise the main objects of the book. Throughout the text, a generally sufficient "linear experience" of readers is exploited, with a special attention to the algebraic aspects of the main mathematical constructions and to practical rules of obtaining new solutions. Various linear equations of classical and quantum mechanics are solved by the Darboux and factorization methods. An extension of the classical Darboux transformations to nonlinear equations in 1+1 and 2+1 dimensions, as well as its factorization are discussed in detail. The applicability of the local and non-local Riemann-Hilbert problem-based approach and its generalization in terms of the d-bar method are illustrated on various nonlinear equations |
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| Description: | Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| ISBN: | 9781402061400 |
| ISSN: | 2352-3905 |
| Accès: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |