LEADER 03806nam 22005895 450 001 9910299780203321 005 20251116133845.0 010 $a1-4939-2181-9 024 7 $a10.1007/978-1-4939-2181-2 035 $a(CKB)3710000000324982 035 $a(SSID)ssj0001408281 035 $a(PQKBManifestationID)11766018 035 $a(PQKBTitleCode)TC0001408281 035 $a(PQKBWorkID)11346384 035 $a(PQKB)10923605 035 $a(DE-He213)978-1-4939-2181-2 035 $a(MiAaPQ)EBC6313115 035 $a(MiAaPQ)EBC5576248 035 $a(Au-PeEL)EBL5576248 035 $a(OCoLC)899265028 035 $a(PPN)183153197 035 $a(EXLCZ)993710000000324982 100 $a20141215d2015 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aIntroduction to Nonlinear Dispersive Equations /$fby Felipe Linares, Gustavo Ponce 205 $a2nd ed. 2015. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d2015. 215 $a1 online resource (XIV, 301 p. 1 illus.) 225 1 $aUniversitext,$x0172-5939 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a1-4939-2180-0 327 $a1. The Fourier Transform -- 2. Interpolation of Operators -- 3. Sobolev Spaces and Pseudo-Differential Operators -- 4. The Linear Schrodinger Equation -- 5. The Non-Linear Schrodinger Equation -- 6. Asymptotic Behavior for NLS Equation -- 7. Korteweg-de Vries Equation -- 8. Asymptotic Behavior for k-gKdV Equations -- 9. Other Nonlinear Dispersive Models -- 10. General Quasilinear Schrodinger Equation -- Proof of Theorem 2.8 -- Proof of Lemma 4.2 -- References -- Index. 330 $aThis textbook introduces the well-posedness theory for initial-value problems of nonlinear, dispersive partial differential equations, with special focus on two key models, the Korteweg?de Vries equation and the nonlinear Schrödinger equation. A concise and self-contained treatment of background material (the Fourier transform, interpolation theory, Sobolev spaces, and the linear Schrödinger equation) prepares the reader to understand the main topics covered: the initial-value problem for the nonlinear Schrödinger equation and the generalized Korteweg?de Vries equation, properties of their solutions, and a survey of general classes of nonlinear dispersive equations of physical and mathematical significance. Each chapter ends with an expert account of recent developments and open problems, as well as exercises. The final chapter gives a detailed exposition of local well-posedness for the nonlinear Schrödinger equation, taking the reader to the forefront of recent research. The second edition of Introduction to Nonlinear Dispersive Equations builds upon the success of the first edition by the addition of updated material on the main topics, an expanded bibliography, and new exercises. Assuming only basic knowledge of complex analysis and integration theory, this book will enable graduate students and researchers to enter this actively developing field. 410 0$aUniversitext,$x0172-5939 606 $aDifferential equations, Partial 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 615 0$aDifferential equations, Partial. 615 14$aPartial Differential Equations. 676 $a515.353 700 $aLinares$b Felipe$4aut$4http://id.loc.gov/vocabulary/relators/aut$0505907 702 $aPonce$b Gustavo$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299780203321 996 $aIntroduction to Nonlinear Dispersive Equations$92503201 997 $aUNINA