Symmetry and Perturbation Theory in Nonlinear Dynamics (Lecture Notes in Physics Monographs)

From the of view of nonlinear. Lecture Notes in Physics Monographs. Free Preview. © Symmetry and Perturbation Theory in Nonlinear Dynamics.
Table of contents

Lamb, and Martin Rasmussen, Bifurcation analysis of a stochastically driven limit cycle. Lamb, and Kevin N. Lamb, Martin Rasmussen, and Christian S. Shilnikov, and Dmitry Turaev, Scientific heritage of L. Lukyanov, and Ivan I. Ovsyannikov, and Joan C. Shilnikov, and Dmitry V. Gonchenko and Ivan I.

Lamb, Dynamics and bifurcations of nonsmooth systems: Proceedings of the International Congress of Mathematicians. Lamb, and Bob W. Beardmore and Kevin N. Shilnikov, and Dmitry Turaev, On dynamical properties of multidimensional diffeomorphisms from Newhouse regions. Lamb, Saddle-nodes and period-doublings of Smale horseshoes: Gonchenko, Dmitry Turaev, and Leonid P.

Dias and Jeroen S. Wavetrains in inhomogeneous moving media , Proc. Geometric aspects of degenerate modulation equations , Stud. Periodic patterns, linear instability, symplectic structure and mean-flow dynamics for three-dimensional surface waves, Phil. Multi-symplectic structures and wave propagation , Math. A geometric formulation of the conservation of wave action and its implications for signature and the classification of instabilities , Proc. Transverse instability of solitary-wave states of the water-wave problem , J.

Superharmonic instability, homoclinic torus bifurcation and water-wave breaking , J. Canonical multi-symplectic structure on the total exterior algebra bundle , Proc. Geometric lift of paths of Hamiltonian equilibria and homoclinic bifurcation , Int. Bifurcation Chaos 22 Emergence of unsteady dark solitary waves from coalescing spatially-periodic patterns , Proc. A universal form for the emergence of the Korteweg-de Vries equation , Proc. A Bifurcation from rolls to multi-pulse planforms via reduction to a parabolic Boussinesq model , Physica D 8—18 Emergence of dispersion in shallow water hydrodynamics via modulation of uniform flow , J.

Breakdown of the Whitham modulation theory and the emergence of dispersion , Stud. Unstable eigenvalues and the linearization about solitary waves and fronts with symmetry , Proc. Degenerate periodic orbits and homoclinic torus bifurcation , Phys. Secondary criticality of water waves. Definition, bifurcation and solitary waves , J.

Quantum Fields on the Lattice

Criticality manifolds and their role in the generation of solitary waves for two-layer flow with a free surface , Euro. Reappraisal of criticality for two-layer flows and its role in the generation of internal solitary waves , Phys. Fluids 19 Variational principles for water waves from the viewpoint of a time-dependent moving mesh , Mathematika 57 , — Multisymplectic structures and the variational bicomplex , Math. Multisymplectic relative equilibria, multiphase wavetrains, and coupled NLS equations , Stud.

Degenerate hyperbolic conservation laws with dissipation: Double criticality and the two-way Boussinesq equation in stratified shallow water hydrodynamics , Phys. Fluids 28 The Hamiltonian double-zero eigenvalue , Fields Inst. Existence and conditional energetic stability of three-dimensional fully localised solitary gravity-capillary water waves , J.

Symmetry, Phase Modulation and Nonlinear Waves

On the geometry of multisymplectic manifolds , J. A 66 — A Tentative Dictionary , ed. On slowly-varying Stokes waves , J. Effect of Krein signatures on the stability of relative equilibria , Cel. Convection patterns in large aspect ratio systems , Physica D 10 — Invariant theory and normal form of Hamiltonian vectorfields with nilpotent linear part , Can. Water wave propagation over uneven bottoms. Part 2 — Non-linear wave propagation , World Scientific Publisher: On two-dimensional packets of capillary-gravity waves , J.

An Introduction , Cambridge University Press: Three-phase solutions of the Kadomtsev-Petviashvili equation , Stud. Validity of Whitham's equations for the modulation of periodic traveling waves in the NLS equation , J. A note on the application of Whitham's method to nonlinear waves in dispersive media , J.

Quantum Fields on the lattice

Strong selection or rejection of spatially periodic patterns in degenerate bifurcations , Physica D 39 — Resolution of a shock in hyperbolic systems modified by weak dispersion , Chaos 15 Unified approach to KdV modulations , Comm. The geometry of the phase-diffusion equation , J. An examination of Whitham's exact averaged variational principle , Proc. Radiation of linear waves in the stationary flow of a Bose-Einstein condensate past an obstacle , Phys.

C Programming

A 75 Momentum maps and classical fields. Weakly non-linear, slowly varying waves and their instabilities , Proc. Models for long-wave instability due to a resonance between two waves, in Trends in Appl. Short-wave instability in a three-layer stratified shear flow , Quart. Long-wave instability in a three-layer stratified shear flow , Stud. Korteweg-de Vries equation, in Nonlinear Waves in Fluids: Recent Advances and Modern Applications , ed.

On variational formulation of periodic and quasi-periodic Hamiltonian motions as relative equilibria, in Geometry and Analysis in Nonlinear Dynamics , eds. Nonstationary structure of a collisionless shock wave , Sov.

Lattice theory

JETP 38 — Introduction to Symplectic Dirac Operators , Lect. Two-dimensional periodic waves in shallow water , J.


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Twodimensional periodic waves in shallow water. Asymmetric waves , J. Conservation of action and modal wave action , Proc. Group velocity and nonlinear dispersive wave propagation , Proc.


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Exact N-soliton solutions of the wave equation of long waves in shallow water and in nonlinear lattices , J. Giampaolo Cicogna , Guiseppe Gaeta. From the of view of nonlinear perturbation theory point the use of has become dynamics, widespread only through equivariant symmetry bifurcation in this attention has been confined to linear even theory; case, mostly symmetries. In this look the basic tools of i.

We focus on the most symmetries, basic fixed the and i. Reduction and Solution of Ordinary Differential Equations. Singular Points and Invariant Manifolds. Symmetries of Dynamical Systems. The Case of dDimensional Algebras of Symmetries. Perturbative Construction of Symmetries. The Normality of the Homological Operator. Convergence of the Normalizing Transformations.