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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Physik & Astronomie Theoretische Physik Transverse Instability of Solitary Waves
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Transverse Instability of Solitary Waves
Timothy J. Burchell, Thomas J. Bridges (Gebundene Ausgabe, Englisch)
Optischer Zustand
Beschreibung
This book presents a wide-ranging geometric approach to the stability of solitary wave solutions of Hamiltonian partial differential equations (PDEs). It blends original research with background material and a review of the literature. The overarching aim is to integrate geometry, algebra, and analysis into a theoretical framework for the spectral problem associated with the transverse instability… of line solitary wave solutions—waves that travel uniformly in a horizontal plane and are embedded in two spatial dimensions. Rather than focusing on individual PDEs, the book develops an abstract class of Hamiltonian PDEs in two spatial dimensions and time, based on multisymplectic Dirac operators and their generalizations. This class models a broad range of nonlinear wave equations and benefits from a distinct symplectic structure associated with each spatial dimension and time. These structures inform both the existence theory (via variational principles, the Maslov index, and transversality conditions) and the linear stability analysis (through a multisymplectic partition of the Evans function). The spectral problem arising from linearization about a solitary wave is formulated as a dynamical system, with three symplectic structures contributing to the analysis. A two-parameter Evans function—depending on the spectral parameter and transverse wavenumber—is constructed from this system. This structure enables new results concerning the Evans function and the linear transverse instability of solitary waves. A key result is an abstract derivative formula for the Evans function in the regime of small stability exponents and transverse wavenumbers. To illustrate the theory, the book introduces a class of vector-valued nonlinear wave equations in 2+1 dimensions that are multisymplectic and admit explicit solitary wave solutions. In this example, the stable and unstable subspaces involved in the Evans function construction are each four-dimensional and can be explicitly computed. The example is used to demonstrate the geometric instability condition and to explore the inner workings of the theory in detail. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
25.11.2025
Sprache
Englisch
EAN
9789819520459
Herausgeber
Springer Singapore
Serien- oder Bandtitel
Mathematical Physics Studies
Sonderedition
Nein
Autor
Timothy J. Burchell, Thomas J. Bridges
Seitenanzahl
164
Einbandart
Gebundene Ausgabe
Buch Untertitel
Multisymplectic Dirac Operators and the Evans Function
Schlagwörter
solitary waves, Hamiltonian PDEs, multisymplectic, linear stability of waves, geometry of the Evans function
Thema-Inhalt
PHU - Mathematische Physik
Höhe
235 mm
Breite
15.5 cm
Transparenz & Sicherheit
Hersteller: Springer, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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