Ebook: Partially Intergrable Evolution Equations in Physics

In the many physical phenomena ruled by partial differential equations, two extreme fields are currently overcrowded due to recent considerable developments: 1) the field of completely integrable equations, whose recent advances are the inverse spectral transform, the recursion operator, underlying Hamiltonian structures, Lax pairs, etc 2) the field of dynamical systems, often built as models of observed physical phenomena: turbulence, intermittency, Poincare sections, transition to chaos, etc. In between there is a very large region where systems are neither integrable nor nonintegrable, but partially integrable, and people working in the latter domain often know methods from either 1) or 2). Due to the growing interest in partially integrable systems, we decided to organize a meeting for physicists active or about to undertake research in this field, and we thought that an appropriate form would be a school. Indeed, some of the above mentioned methods are often adaptable outside their original domain and therefore worth to be taught in an interdisciplinary school. One of the main concerns was to keep a correct balance between physics and mathematics, and this is reflected in the list of courses.

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Content:
Front Matter....Pages i-xvii
Competing Interactions and Complexity in Condensed Matter....Pages 1-38
Exact Solutions of the Boltzmann Equation....Pages 39-82
Nonlinear Interaction Between Short and Long Waves....Pages 83-159
Nonlinear Optics....Pages 161-161
The Phase Diffusion and Mean Drift Equations for Convection at Finite Rayleigh Numbers in Large Containers I....Pages 163-163
Nonlinear Evolution Equations, Quasi-Solitons and their Experimental Manifestation....Pages 165-221
The Initial-Boundary Value Problem for the Davey-Stewartson 1 Equation; How to Generate and Drive Localized Coherent Structures in Multidimensions....Pages 223-259
Ginzburg-Landau models of non-equilibrium....Pages 261-275
Nonlinear Ginzburg-Landau equation and its applications to fluid-mechanics....Pages 277-278
Defects and Disorder of Non-Linear Waves in Convection....Pages 279-296
An Introduction to Kowalevski’s Exponents....Pages 299-320
Singularity Analysis and its Relation to Complete, Partial and Non-Integrability....Pages 321-372
A Concept of Integrability Based on the Symmetry Approach....Pages 373-373
B?cklund Transformations and the Painlev? property....Pages 375-411
Differential Geometry Techniques for Sets of Nonlinear Partial Differential Equations....Pages 413-434
Inertial Manifolds and Attractors of Partial Differential Equations....Pages 435-458
Hirota’s Bilinear Method and Partial Integrability....Pages 459-478
Generalized Symmetries, Recursion Operators and Bihamiltonian Systems....Pages 479-489
Nonlinear Dispersive Equations without Inverse Scattering....Pages 491-513
Group Theory and exact Solutions of Partially Integrable Differential Systems....Pages 515-567
The Nonlinear Evolution Equation for the Order Parameter in Superfluid Helium-Four....Pages 569-570
Quasimonomial Transformations and Integrability....Pages 571-572
Partial Integrability of the Damped Kink Equation....Pages 573-574
New Similarity Reductions of Boussinesq-Type Equations....Pages 575-576
The Homographic Invariance of PDE Painlev? Analysis....Pages 577-578
The Nonlocal Amplitude Equation....Pages 579-580
Pressure Waves in Fluid-Filled Nonlinear Viscoelastic Tubes....Pages 581-582
Elliptic Function Solutions for Landau-Ginzburg Equation....Pages 583-584
Application of a Macsyma Program for the Painlev? Test to the Fitzhugh-Nagumo Equation....Pages 585-586
The Strongly Dissipative Toda Lattice....Pages 587-588
A Perturbative Approach to Hirota’s Bilinear Equations of KdV-Type....Pages 589-590
Construction of Two Dimensional Super Potentials for Classical Super Systems....Pages 591-592
Applications of Nonlinear PDE’s to the Modelling of Ferromagnetic Inhomogeneities....Pages 593-594
Back Matter....Pages 595-605

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Content:
Front Matter....Pages i-xvii
Competing Interactions and Complexity in Condensed Matter....Pages 1-38
Exact Solutions of the Boltzmann Equation....Pages 39-82
Nonlinear Interaction Between Short and Long Waves....Pages 83-159
Nonlinear Optics....Pages 161-161
The Phase Diffusion and Mean Drift Equations for Convection at Finite Rayleigh Numbers in Large Containers I....Pages 163-163
Nonlinear Evolution Equations, Quasi-Solitons and their Experimental Manifestation....Pages 165-221
The Initial-Boundary Value Problem for the Davey-Stewartson 1 Equation; How to Generate and Drive Localized Coherent Structures in Multidimensions....Pages 223-259
Ginzburg-Landau models of non-equilibrium....Pages 261-275
Nonlinear Ginzburg-Landau equation and its applications to fluid-mechanics....Pages 277-278
Defects and Disorder of Non-Linear Waves in Convection....Pages 279-296
An Introduction to Kowalevski’s Exponents....Pages 299-320
Singularity Analysis and its Relation to Complete, Partial and Non-Integrability....Pages 321-372
A Concept of Integrability Based on the Symmetry Approach....Pages 373-373
B?cklund Transformations and the Painlev? property....Pages 375-411
Differential Geometry Techniques for Sets of Nonlinear Partial Differential Equations....Pages 413-434
Inertial Manifolds and Attractors of Partial Differential Equations....Pages 435-458
Hirota’s Bilinear Method and Partial Integrability....Pages 459-478
Generalized Symmetries, Recursion Operators and Bihamiltonian Systems....Pages 479-489
Nonlinear Dispersive Equations without Inverse Scattering....Pages 491-513
Group Theory and exact Solutions of Partially Integrable Differential Systems....Pages 515-567
The Nonlinear Evolution Equation for the Order Parameter in Superfluid Helium-Four....Pages 569-570
Quasimonomial Transformations and Integrability....Pages 571-572
Partial Integrability of the Damped Kink Equation....Pages 573-574
New Similarity Reductions of Boussinesq-Type Equations....Pages 575-576
The Homographic Invariance of PDE Painlev? Analysis....Pages 577-578
The Nonlocal Amplitude Equation....Pages 579-580
Pressure Waves in Fluid-Filled Nonlinear Viscoelastic Tubes....Pages 581-582
Elliptic Function Solutions for Landau-Ginzburg Equation....Pages 583-584
Application of a Macsyma Program for the Painlev? Test to the Fitzhugh-Nagumo Equation....Pages 585-586
The Strongly Dissipative Toda Lattice....Pages 587-588
A Perturbative Approach to Hirota’s Bilinear Equations of KdV-Type....Pages 589-590
Construction of Two Dimensional Super Potentials for Classical Super Systems....Pages 591-592
Applications of Nonlinear PDE’s to the Modelling of Ferromagnetic Inhomogeneities....Pages 593-594
Back Matter....Pages 595-605
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