Virtual Turning Points II Their Interplay with Integral Representations and Non-Hereditary Turning Points /
This book aims to build on the significant results reported since the publication of "Virtual Turning Points" (VTP). This volume seeks to accelerate this trend by presenting these results in a unified manner, utilizing s-VTP and the integral representation of solutions. This includes the i...
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| 語言: | 英语 |
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Singapore :
Springer Nature Singapore : Imprint: Springer,
2025.
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| 版: | 1st ed. 2025. |
| 叢編: | SpringerBriefs in Mathematical Physics,
52 |
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| 在線閱讀: | https://doi.org/10.1007/978-981-95-2817-2 |
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| 100 | 1 | |a Hirose, Sampei. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Virtual Turning Points II |h [electronic resource] : |b Their Interplay with Integral Representations and Non-Hereditary Turning Points / |c by Sampei Hirose, Naofumi Honda, Takahiro Kawai, Shinji Sasaki, Yoshitsugu Takei. |
| 250 | |a 1st ed. 2025. | ||
| 264 | 1 | |a Singapore : |b Springer Nature Singapore : |b Imprint: Springer, |c 2025. | |
| 300 | |a 1 online resource (XII, 106 p. 1 illus.). | ||
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| 505 | 0 | |a 1 Integral Representation of Solutions and Related Topics -- 2 Degeneration of the Stokes Geometry for Higher-Order Equations -- 3 A Bicharacteristic Chain Associated with a Non-hereditary Turning Point -- Appendix A: Confirmation of the Activeness of Some Stokes Curves by Using the Exact Steepest Descent Method. | |
| 520 | |a This book aims to build on the significant results reported since the publication of "Virtual Turning Points" (VTP). This volume seeks to accelerate this trend by presenting these results in a unified manner, utilizing s-VTP and the integral representation of solutions. This includes the introduction of a non-hereditary turning point (NHTP), which naturally appears by considering tangential systems. NHTP initially causes no issues for the original system, but it creates a new class of VTPs and additional periods when perturbing the equation while keeping its principal part intact. Integral representations of solutions provide intriguing examples of Stokes geometry (SG). We have selected some particularly illuminating examples and presented them in Sect. 1.5 to address the effects of NHTP and the crossing phenomenon of three ordinary Stokes curves, which were not dealt with in VTP. The most important example suggests that these new phenomena are related to the location of singularities of Borel transformed WKB solutions. Comparing with the second-order case, we study this relationship from the viewpoint of the theory of growing trees already discussed in VTP. These examples also reveal an impressive fact that NHTP creates a new class of VTPs through the so-called bicharacteristic chain. Another example visualizes a leaf-type and a tadpole-type SG, the connection formulas for which are explicitly computed in this volume. Finally in the Appendix, the activeness of SG related to the crossing of three Stokes curves is examined, which requires employment of the exact steepest descent method, a WKB-theoretical generalization of the traditional steepest descent method, despite its simple appearance. | ||
| 532 | 8 | |a Accessibility summary: This PDF has been created in accordance with the PDF/UA-1 standard to enhance accessibility. It includes screen reader support, descriptions for Non-text content (such as images and graphs), bookmarks for easy navigation, keyboard-friendly links and forms, and searchable, selectable text. We recognise the importance of accessibility and welcome queries about accessibility for any of our products. If you have a question or an access need, please get in touch with us via https://www.springernature.com/gp/info/accessibility Please Note that a more accessible version of this eBook is available as an EPUB. | |
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| 700 | 1 | |a Honda, Naofumi. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 700 | 1 | |a Kawai, Takahiro. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 700 | 1 | |a Sasaki, Shinji. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 700 | 1 | |a Takei, Yoshitsugu. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
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