Self-Similarity and Beyond

Exact Solutions of Nonlinear Problems

P.L. Sachdev

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English

Chapman & Hall/CRC
18 December 2020

Numerical analysis; Non-linear science; Maths for scientists; Maths for engineers

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.

By: P.L. Sachdev
Imprint: Chapman & Hall/CRC
Country of Publication: United Kingdom
Dimensions: Height: 234mm, Width: 156mm,
Weight: 453g
ISBN: 9780367455484
ISBN 10: 036745548X
Pages: 336
Publication Date: 18 December 2020
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Sachdev, P.L.