03271nam 22006852 450 991045771720332120160427170801.01-107-15013-21-280-54012-597866105401290-511-21484-70-511-21663-70-511-21126-00-511-31541-40-511-54304-20-511-21303-4(CKB)1000000000353015(EBL)266622(OCoLC)171139024(SSID)ssj0000139444(PQKBManifestationID)11136745(PQKBTitleCode)TC0000139444(PQKBWorkID)10010925(PQKB)10386330(UkCbUP)CR9780511543043(MiAaPQ)EBC266622(Au-PeEL)EBL266622(CaPaEBR)ebr10131623(CaONFJC)MIL54012(OCoLC)124039379(EXLCZ)99100000000035301520090505d2004|||| uy| 0engur|||||||||||txtrdacontentcrdamediacrrdacarrierThe direct method in soliton theory /Ryogo Hirota ; translated from Japanese and edited by Atsushi Nagai, Jon Nimmo, and Claire Gilson[electronic resource]Cambridge :Cambridge University Press,2004.1 online resource (xi, 200 pages) digital, PDF file(s)Cambridge tracts in mathematics ;155Title from publisher's bibliographic system (viewed on 05 Oct 2015).0-521-83660-3 Includes bibliographical references (p. 195-197) and index.1. Bilinearization of soliton equations -- 2. Determinants and pfaffians -- 3. Structure of soliton equations -- 4. Backlund transformations -- Afterword -- References -- Index.The bilinear, or Hirota's direct, method was invented in the early 1970s as an elementary means of constructing soliton solutions that avoided the use of the heavy machinery of the inverse scattering transform and was successfully used to construct the multisoliton solutions of many new equations. In the 1980s the deeper significance of the tools used in this method - Hirota derivatives and the bilinear form - came to be understood as a key ingredient in Sato's theory and the connections with affine Lie algebras. The main part of this book concerns the more modern version of the method in which solutions are expressed in the form of determinants and pfaffians. While maintaining the original philosophy of using relatively simple mathematics, it has, nevertheless, been influenced by the deeper understanding that came out of the work of the Kyoto school. The book will be essential for all those working in soliton theory.Cambridge tracts in mathematics ;155.SolitonsSolitons.530.12/4Hirota Ryōgo1932-291230Nagai AtsushiNimmo J. J. C(Jonathan J. C.),Gilson ClaireUkCbUPUkCbUPBOOK9910457717203321Direct method in soliton theory748606UNINA03362oam 2200457 450 991029996210332120190911103512.01-4614-8866-410.1007/978-1-4614-8866-8(OCoLC)863045384(MiFhGG)GVRL6YOM(EXLCZ)99255000000115114720130819d2014 uy 0engurun|---uuuuatxtccrWaves in neural media from single neurons to neural fields /Paul C. Bressloff1st ed. 2014.New York :Springer,2014.1 online resource (xix, 436 pages) illustrations (some color)Lecture Notes on Mathematical Modelling in the Life Sciences,2193-4789"ISSN: 2193-4789.""ISSN: 2193-4797 (electronic)."1-4614-8865-6 Includes bibliographical references and index.Preface -- Part I Neurons -- Single Neuron Modeling -- Traveling Waves in One-Dimensional Excitable Media -- Wave Propagation Along Spiny Dendrites -- Calcium Waves and Sparks -- Part II Networks -- Waves in Synaptically-Coupled Spiking Networks -- Population Models and Neural Fields -- Waves in Excitable Neural Fields -- Neural Field Model of Binocular Rivalry Waves -- Part III Development and Disease -- Waves in the Developing and the Diseased Brain -- Index.Waves in Neural Media: From Single Cells to Neural Fields surveys mathematical models of traveling waves in the brain, ranging from intracellular waves in single neurons to waves of activity in large-scale brain networks. The work provides a pedagogical account of analytical methods for finding traveling wave solutions of the variety of nonlinear differential equations that arise in such models. These include regular and singular perturbation methods, weakly nonlinear analysis, Evans functions and wave stability, homogenization theory and averaging, and stochastic processes. Also covered in the text are exact methods of solution where applicable. Historically speaking, the propagation of action potentials has inspired new mathematics, particularly with regard to the PDE theory of waves in excitable media. More recently, continuum neural field models of large-scale brain networks have generated a new set of interesting mathematical questions with regard to the solution of nonlocal integro-differential equations.  Advanced graduates, postdoctoral researchers and faculty working in mathematical biology, theoretical neuroscience, or applied nonlinear dynamics will find this book to be a valuable resource. The main prerequisites are an introductory graduate course on ordinary differential equations and partial differential equations, making this an accessible and unique contribution to the field of mathematical biology. .Lecture notes on mathematical modelling in the life sciences.Neural networks (Neurobiology)Neural networks (Neurobiology)006.3006.32Bressloff Paul Cauthttp://id.loc.gov/vocabulary/relators/aut721730MiFhGGMiFhGGBOOK9910299962103321Waves in neural media1410729UNINA