# Mathematics of Nonlinear Science

Share this page *Edited by *
*Melvyn S. Berger*

This volume contains the proceedings of an AMS Special Session on the
Mathematics of Nonlinear Science, held in Phoenix in January 1989. This area
of research encompasses a large and rapidly growing set of ideas concerning the
relationship of mathematics to science, in which the fundamental laws of nature
are extended beyond common sense into new areas where the dual aspects of order
and chaos abound.

These papers, generally analytic in nature, deal primarily with mathematical
aspects of physical science and non-chaotic phenomenon. Important new areas
are discussed, such as instability, global extensions of KAM theory, new ideas
concerning integrable systems, bifurcation and its applications in fluids,
and various aspects of gauge theory. Altogether, the topics explored here
represent an excellent survey of some of the new research in the mathematics of
nonlinear science.

# Table of Contents

## Mathematics of Nonlinear Science

- Contents ix10 free
- Preface xi12 free
- Multiple steady states in tubular chemical reactors 114 free
- Two new approaches to large amplitude quasi-periodic motions of certain nonlinear Hamiltonian systems 1124
- Vortices for the Ginzburg-Landau equations–the nonsymmetric case in bounded domain 1932
- Nonlinear stability and bifurcation in Hamiltonian systems with symmetry 3346
- Nonlinear resonance in inhomogeneous systems of conservation laws 6376
- Bifurcation and stability in rotating, plane Couette-Poiseuille flow 7992
- Bifurcations of central configurations in the N -body problem 93106
- Leapfrogging of vortex filaments in an ideal fluid 103116
- Calculation of sharp shocks using Sobolev gradients 111124
- Monodromy preserving deformation of the Dirac operator acting on the hyperbolic plane 119132
- Bifurcation from equilibria for certain infinite-dimensional dynamical systems 133146
- On dynamics of discrete and continuous σ-models (chiral fields) with values in Riemannian manifolds 139152
- Direct study for some nonlinear elliptic control problems 145158