This book is a unique selection of work by world-class experts exploring the latest developments in Hamiltonian partial differential equations and their applications. Topics covered within are representative of the field’s wide scope, including KAM and normal form theories, perturbation and variational methods, integrable systems, stability of nonlinear solutions as well as applications to cosmology, fluid mechanics and water waves.
The volume contains both surveys and original research papers and gives a concise overview of the above topics, with results ranging from mathematical modeling to rigorous analysis and numerical simulation. It will be of particular interest to graduate students as well as researchers in mathematics and physics, who wish to learn more about the powerful and elegant analytical techniques for Hamiltonian partial differential equations.
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Hamiltonian Structure, Fluid Representation and Stability for the Vlasov–Dirac–Benney Equation (C. Bardos, N. Besse).- Analysis of Enhanced Diffusion in Taylor Dispersion via a Model Problem (M. Beck, O. Chaudhary, C.E. Wayne).- Normal Form Transformations for Capillary-Gravity Water Waves (W. Craig, C. Sulem).- On a Fluid-Particle Interaction Model: Global in Time Weak Solutions Within a Moving Domain in R3 (S. Doboszczak, K. Trivisa).- Envelope Equations for Three-Dimensional Gravity and Flexural-Gravity Waves Based on a Hamiltonian Approach (P. Guyenne).- Dissipation of a Narrow-Banded Surface Water Waves (D. Henderson, G.K. Rajan, H. Segur).- The Kelvin–Helmholtz Instabilities in Two-Fluids Shallow Water Models (D. Lannes, M. Ming).- Some Analytic Results on the FPU Paradox (D. Bambusi, A. Carati, A. Maiocchi, A. Maspero).- A Nash–Moser Approach to KAM Theory (M. Berti, P. Bolle).- On the Spectral and Orbital Stability of Spatially Periodic Stationary Solutions of Generalized Korteweg–de Vries Equations (T. Kapitula, B. Deconinck).- Time-Averaging for Weakly Nonlinear CGL Equations with Arbitrary Potentials (G. Huang, S. Kuksin, A. Maiocchi).- Partial Differential Equations with Random Noise in Inflationary Cosmology (R.H. Brandenberger).- Local Isometric Immersions of Pseudo-Spherical Surfaces and Evolution Equations (N. Kahouadji, N. Kamran, K. Tenenblat).- IST Versus PDE, A Comparative Study (C. Klein, J.-C. Saut).
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