Drazin, P. G.; Johnson, R. S. Solitons: an introduction. (English) Zbl 0661.35001 Cambridge Texts in Applied Mathematics. Cambridge etc.: Cambridge University Press. xii, 226 p. £32.50/hbk; £11.95/pbk; $ 59.50/hbk $ 19.95/pbk (1989). This is a well written and relatively simple textbook on the inverse scattering transform and related topics for senior undergraduate students. Basic attention is paid to the Korteweg-de Vries equation. Besides the inverse scattering transform proper (including its generalizations in the Ablowitz - Kaup - Newell - Segur and Zakharov - Shabat forms), some special issues, such as Hirota’s method, the Bäcklund transformation, and the Painlevé property, are addressed. Each chapter is completed by useful exercises. In the end of the book, answers to those exercises are given. Reviewer: B.A.Malomed Cited in 423 Documents MSC: 35-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to partial differential equations 35Q99 Partial differential equations of mathematical physics and other areas of application 35A30 Geometric theory, characteristics, transformations in context of PDEs Keywords:inverse scattering transform; Korteweg-de Vries equation; Hirota’s method; Bäcklund transformation; Painlevé property PDF BibTeX XML Cite \textit{P. G. Drazin} and \textit{R. S. Johnson}, Solitons: an introduction. Cambridge etc.: Cambridge University Press (1989; Zbl 0661.35001) OpenURL Digital Library of Mathematical Functions: §22.19(iii) Nonlinear ODEs and PDEs ‣ §22.19 Physical Applications ‣ Applications ‣ Chapter 22 Jacobian Elliptic Functions Chapter 22 Jacobian Elliptic Functions