Self-Similarity and Beyond

Exact Solutions of Nonlinear Problems
1. Auflage 2000
ISBN: 978-1-58488-211-4
Verlag: Taylor & Francis Inc

Buch, Englisch, 336 Seiten, Format (B × H): 163 mm x 242 mm, Gewicht: 635 g

Reihe: Monographs and Surveys in Pure and Applied Mathematics

Nonlinearity plays a major role in the understanding of most physical, chemical, biological, and engineering sciences.
Nonlinear problems fascinate scientists and engineers, but often elude exact treatment. However elusive they may be, the solutions do exist-if only one perseveres in seeking them out.

Self-Similarity and Beyond presents a myriad of approaches to finding exact solutions for a diversity of nonlinear problems. These include group-theoretic methods, the direct method of Clarkson and Kruskal, traveling waves, hodograph methods, balancing arguments, embedding special solutions into a more general class, and the infinite series approach.

The author's approach is entirely constructive. Numerical solutions either motivate the analysis or confirm it, therefore they are treated alongside the analysis whenever possible. Many examples drawn from real physical situations-primarily fluid mechanics and nonlinear diffusion-illustrate and emphasize the central points presented.

Accessible to a broad base of readers, Self-Similarity and Beyond illuminates a variety of productive methods for meeting the challenges of nonlinearity. Researchers and graduate students in nonlinearity, partial differential equations, and fluid mechanics, along with mathematical physicists and numerical analysts, will re-discover the importance of exact solutions and find valuable additions to their mathematical toolkits.

Zielgruppe

Academic and Professional Practice & Development

Autoren/Hrsg.

Sachdev, P.L.

Fachgebiete

• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Mathematik | Informatik Mathematik Mathematische Analysis Moderne Anwendungen der Analysis
• Naturwissenschaften Biowissenschaften Angewandte Biologie Biomathematik

Inhaltsverzeichnis

Introduction. First Order Partial Differential Equations. Exact Similarity Solutions of Nonlinear PDEs. Exact Travelling Wave Solutions. Exact Linearization of Nonlinear PDEs. Nonlinearization and Embedding of Special Solutions. Asymptotic Solutions by Balancing Arguments. Series Solutions of Nonlinear PDEs.

Über Autor(innen)

Sachdev, P.L.