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Dynamics --- Nonlinear theories --- Dynamique --- Théories non linéaires --- Fluctuations (Physics) --- #KVIV:BB --- Nonlinear problems --- Nonlinearity (Mathematics) --- Calculus --- Mathematical analysis --- Mathematical physics --- Variations (Physics) --- Stochastic processes --- Théories non linéaires --- Fokker-Planck equation --- Equation, Fokker-Planck --- Planck-Fokker equation --- Differential equations, Partial --- Stochastic differential equations

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Stochastic processes --- Differential equations --- Differential equations, Partial --- Differential equations, Parabolic --- Fokker-Planck equation. --- Transport theory. --- Equations aux dérivées partielles --- Equations différentielles paraboliques --- Fokker-Planck, Equation de --- Transport, Théorie du --- Asymptotic theory. --- Théorie asymptotique --- 51 <082.1> --- Mathematics--Series --- Equations aux dérivées partielles --- Equations différentielles paraboliques --- Transport, Théorie du --- Théorie asymptotique --- Fokker-Planck equation --- Transport theory --- Boltzmann transport equation --- Transport phenomena --- Mathematical physics --- Particles (Nuclear physics) --- Radiation --- Statistical mechanics --- Equation, Fokker-Planck --- Planck-Fokker equation --- Stochastic differential equations --- Asymptotic theory in partial differential equations --- Asymptotic expansions --- Asymptotic theory of parabolic differential equations --- Asymptotic theory --- Développements asymptotiques --- Équations aux dérivées partielles

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Providing an introduction to the theory of nonlinear Fokker-Planck equations, this book discusses fundamental properties of transient and stationary solutions, emphasizing the stability analysis of stationary solutions by means of self-consistency equations, linear stability analysis, and Lyapunov's direct method. Also treated are Langevin equations and correlation functions. Nonlinear Fokker-Planck Equations addresses various phenomena such as phase transitions, multistability of systems, synchronization, anomalous diffusion, cut-off solutions, travelling-wave solutions and the emergence of power law solutions. A nonlinear Fokker-Planck perspective to quantum statistics, generalized thermodynamics, and linear nonequilibrium thermodynamics is given. Theoretical concepts are illustrated where possible by simple examples. The book also reviews several applications in the fields of condensed matter physics, the physics of porous media and liquid crystals, accelerator physics, neurophysics, social sciences, population dynamics, and computational physics.

Fokker-Planck equation. --- Stochastic differential equations. --- Differential equations, Nonlinear. --- Nonlinear differential equations --- Nonlinear theories --- Differential equations --- Fokker-Planck equation --- Equation, Fokker-Planck --- Planck-Fokker equation --- Differential equations, Partial --- Stochastic differential equations --- Quantum theory. --- Distribution (Probability theory. --- Mathematical physics. --- Thermodynamics. --- Statistical physics. --- Quantum Physics. --- Complex Systems. --- Probability Theory and Stochastic Processes. --- Mathematical Methods in Physics. --- Statistical Physics and Dynamical Systems. --- Physics --- Mathematical statistics --- Chemistry, Physical and theoretical --- Dynamics --- Mechanics --- Heat --- Heat-engines --- Quantum theory --- Physical mathematics --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Thermodynamics --- Statistical methods --- Mathematics --- Quantum physics. --- Dynamical systems. --- Probabilities. --- Physics. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Risk --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Statics