{"product_id":"the-painleve-handbook-practical-guide-to-singularity-analysis","title":"The Painleve Handbook - Practical Guide to Singularity Analysis","description":"\u003cp\u003eIn this review of The Painleve Handbook, the reviewer finds a rigorous and practical reference aimed at mathematicians and physicists working with nonlinear differential and difference equations; the single biggest reason to buy is its clear demonstration of how \u003cstrong\u003ePainleve analysis\u003c\/strong\u003e becomes an algorithmic tool to construct explicit solutions to integrable and physically relevant equations. This second edition is noticeably updated and expanded, making it a useful companion for researchers and advanced graduate students who need direct worked examples and recent theoretical context to apply singularity analysis.\u003c\/p\u003e\u003ch2\u003eKey Features\u003c\/h2\u003e\u003cul\u003e\n\u003cli\u003e\n\u003cstrong\u003eComprehensive exposition:\u003c\/strong\u003e The book walks through the singularity analysis of differential and difference equations step by step, helping readers apply the Painleve test in practical problems.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eAlgorithmic approach:\u003c\/strong\u003e Emphasis on algorithmic construction of explicit solutions makes the methods reproducible for both ordinary and partial differential equations.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eIllustrative examples:\u003c\/strong\u003e Integrable equations such as the nonlinear Schrodinger and Korteweg-de Vries equations are treated in detail to show method application.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003ePhysically relevant cases:\u003c\/strong\u003e Numerous examples, including the Kuramoto-Sivashinsky and Kolmogorov-Petrovski-Piskunov equations, connect theory to real-world models.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eUpdated theory:\u003c\/strong\u003e The second edition incorporates recent insights from Nevanlinna theory and extended analysis for the cubic and quintic Ginzburg-Landau equations.\u003c\/li\u003e\n\u003c\/ul\u003e\u003ch2\u003eWho It's For\u003c\/h2\u003e\u003cp\u003eThe Painleve Handbook is best for researchers, postdocs, and advanced graduate students in mathematical physics or applied mathematics who already have a solid grounding in differential equations and complex analysis and who want a hands-on guide to \u003cstrong\u003esingularity analysis\u003c\/strong\u003e and explicit solution construction. Its algorithmic orientation and worked examples make it suitable as a desk reference when attacking nonlinear integrable models.\u003c\/p\u003e\u003cp\u003eReaders seeking an introductory textbook on ordinary differential equations or a casual overview of integrable systems should look elsewhere; the book assumes familiarity with advanced material and is not designed as an elementary introduction for beginners.\u003c\/p\u003e\u003ch2\u003ePros \u0026amp; Cons\u003c\/h2\u003e\u003cp\u003e\u003cstrong\u003ePros\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eDetailed, example-driven presentation of the Painleve test that supports reproducible solution methods.\u003c\/li\u003e\n\u003cli\u003eCoverage of both differential and difference equations which broadens applicability to discrete models.\u003c\/li\u003e\n\u003cli\u003eInclusion of modern theoretical context, such as Nevanlinna theory, enhances the second edition's relevance.\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003e\u003cstrong\u003eCons\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\u003cli\u003eThe material presumes advanced background and is not accessible to readers without prior graduate-level training.\u003c\/li\u003e\u003c\/ul\u003e\u003ch2\u003eSpecifications\u003c\/h2\u003e\u003ctable\u003e\n\u003ctr\u003e\n\u003ctd\u003eTitle\u003c\/td\u003e\n\u003ctd\u003eThe Painleve Handbook (Mathematical Physics Studies)\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eAuthors\u003c\/td\u003e\n\u003ctd\u003eRobert Conte, Micheline Musette\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eEdition\u003c\/td\u003e\n\u003ctd\u003eSecond edition, revised and expanded\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eScope\u003c\/td\u003e\n\u003ctd\u003eSingularity analysis of differential and difference equations\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eIllustrated with\u003c\/td\u003e\n\u003ctd\u003eNonlinear Schrodinger, Korteweg-de-Vries, Henon-Heiles, Ginzburg-Landau equations\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eApplications\u003c\/td\u003e\n\u003ctd\u003eKuramoto-Sivashinsky, Kolmogorov-Petrovski-Piskunov, and other physical models\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e\u003ch2\u003eOur Verdict\u003c\/h2\u003e\u003cp\u003eThe Painleve Handbook is a substantial and practical reference for practitioners in mathematical physics who need a rigorous, example-rich guide to \u003cstrong\u003ePainleve analysis\u003c\/strong\u003e. While it assumes a high level of background knowledge, its algorithmic focus and updated content make it good value for researchers and advanced students seeking to apply singularity methods to integrable and physically motivated equations.\u003c\/p\u003e\u003ch2\u003eFrequently Asked Questions\u003c\/h2\u003e\u003cp\u003e\u003cstrong\u003eDoes this edition include new material?\u003c\/strong\u003e\u003cbr\u003eYes, the second edition is extensively revised, updated, and expanded and includes recent insights from Nevanlinna theory and expanded analysis for Ginzburg-Landau equations.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eAre worked examples provided?\u003c\/strong\u003e\u003cbr\u003eYes, the book includes detailed examples such as the nonlinear Schrodinger and Korteweg-de-Vries equations and several physically relevant models to illustrate methods.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eIs this suitable for beginners?\u003c\/strong\u003e\u003cbr\u003eNo, the text assumes advanced background in differential equations and complex analysis and is best for graduate-level readers and researchers.\u003c\/p\u003e","brand":"Robert Conte, Micheline Musette","offers":[{"title":"Default Title","offer_id":48183557193947,"sku":"3030533425","price":156.26,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0724\/1043\/1707\/files\/51CfnTS5uzL._SL1254.jpg?v=1769523153","url":"https:\/\/gearmusthave.com\/products\/the-painleve-handbook-practical-guide-to-singularity-analysis","provider":"GearMustHave","version":"1.0","type":"link"}