Nonlinear Stochastic Systems Theory and Applications to Physics

Approach your problems from the right end and begin with the answers. Then one day, perhaps you will find the final answer. "The Hermit Clad In Crane Feathers" In R. van Gullk's The Chinese Haze Hurders. It Isn't that they can't see the solution. It IS that they can't see the problem. G. K. Chesterton. The Scandal of Father Brown. "The POint of a Pin." Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of k now ledge of m athemat i cs and re I ated fie I ds does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, COding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And In addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely Integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the eXisting classificatIOn schemes.

Contenu
I: A Summary of the Decomposition Method.- 1: The Decomposition Method.- 2: Effects of Nonlinearity and Linearization.- 3: Research on Initial and Boundary Conditions for Differential and Partial Differential Equations.- II: Applications to the Equations of Physics.- 4: The Burger's Equation.- 5: Heat Flow and Diffusion.- 6: Nonlinear Oscillations in Physical Systems.- 7: The KdV Equation.- 8: The Benjamin-Ono Equation.- 9: The Sine-Gordon Equation.- 10: The Nonlinear Schrödinger Equation and the Generalized Schrödinger Equation.- 11: Nonlinear Plasmas.- 12: The Tricomi Problem.- 13: The Initial-Value Problem for the Wave Equation.- ChaDter 14: Nonlinear Dispersive or Dissipative Waves.- 15: The Nonlinear Klein-Gordon Equation.- 16: Analysis of Model Equations of Gas Dynamics.- 17: A New Approach to the Efinger Model for a Nonlinear Quantum Theory for Gravitating Particles.- 18: The Navier-Stokes Equations.- Epilogue.