LEADER 04635nam 22006735 450 001 9910847580203321 005 20240415124822.0 010 $a3-031-54978-3 024 7 $a10.1007/978-3-031-54978-6 035 $a(CKB)31491851500041 035 $a(MiAaPQ)EBC31278654 035 $a(Au-PeEL)EBL31278654 035 $a(DE-He213)978-3-031-54978-6 035 $a(EXLCZ)9931491851500041 100 $a20240415d2024 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aFractional Dispersive Models and Applications$b[electronic resource] $eRecent Developments and Future Perspectives /$fedited by Panayotis G. Kevrekidis, Jesús Cuevas-Maraver 205 $a1st ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2024. 215 $a1 online resource (337 pages) 225 1 $aNonlinear Systems and Complexity,$x2196-0003 ;$v37 311 $a3-031-54977-5 327 $aChapter 1. Fractional Dispersive Models and Applications (Panayotis G. Kevrekidis) -- Chapter 2. Fractional Wave Models and Their Experimental Applications (Boris A. Malomed) -- Chapter 3. Fractional Models in Biology and Medicine (Fractional Models in Biology and Medicine) -- Chapter 4. Fractional Dissipative PDEs (Franz Achleitner) -- Chapter 5. Symmetry breaking in fractional nonlinear Schrödinger and soliton dynamics in complex Ginzburg-Landau models (Pengfei Li) -- Chapter 6. Traveling waves in fractional models (Traveling waves in fractional models) -- Chapter 7. Numerical methods for fractional PDEs (Christian Klein) -- Chapter 8. Fractional Non-Linear Quantum Analysis, Probability, Discretization, and Limits (Kay L. Kirkpatrick) -- Chapter 9. Fractional Integrable Dispersive Equations (Mark J. Ablowitz) -- Chapter 10. Fractional discrete linear and nonlinear models (Mario I. Molina) -- Chapter 11. Breathers in the fractionalFrenkel-Kontorova model (J. Catarecha). 330 $aThis book explores the role of fractional calculus and associated partial differential equations in modeling multiscale phenomena and overlapping macroscopic & microscopic scales, offering an innovative and powerful tool for modeling complex systems. While integer order PDEs have a long-standing history, the novel setting of fractional PDEs opens up new possibilities for the simulation of multi-physics phenomena. The book examines a range of relevant examples that showcase the seamless transition from wave propagation to diffusion or from local to non-local dynamics in both continuum and discrete systems. These systems have been argued as being particularly relevant in contexts such as nonlinear optics, lattice nonlinear dynamical systems, and dispersive nonlinear wave phenomena, where the exploration of the potential fractionality has emerged as a highly active topic for current studies. The volume consists of contributions from a diverse group of active scholars and experts across different fields, providing a detailed examination of the field's past, present, and future state-of-the-art in the interplay of fractional PDEs and nonlinear wave phenomena. It is intended to be of wide interest to both seasoned researchers and beginners in the Field of Nonlinear Science. This book sets the stage for the next decade of research and beyond and is a timely and relevant reference of choice for this crucial junction of current research. 410 0$aNonlinear Systems and Complexity,$x2196-0003 ;$v37 606 $aSystem theory 606 $aDifferential equations 606 $aPlasma waves 606 $aNonlinear Optics 606 $aBioinformatics 606 $aComplex Systems 606 $aDifferential Equations 606 $aWaves, instabilities and nonlinear plasma dynamics 606 $aNonlinear Optics 606 $aComputational and Systems Biology 615 0$aSystem theory. 615 0$aDifferential equations. 615 0$aPlasma waves. 615 0$aNonlinear Optics. 615 0$aBioinformatics. 615 14$aComplex Systems. 615 24$aDifferential Equations. 615 24$aWaves, instabilities and nonlinear plasma dynamics. 615 24$aNonlinear Optics. 615 24$aComputational and Systems Biology. 676 $a530.1 700 $aKevrekidis$b Panayotis G$0833959 701 $aCuevas-Maraver$b Jesús$01736273 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910847580203321 996 $aFractional Dispersive Models and Applications$94156141 997 $aUNINA