In the developing area of nonlinear mathematics, there are a large number of classes of nonlinear equations which have received attention. This collection of 11 articles addresses a number of physically motivated systems for which considerable theory is available, such as reaction-diffusion systems and elasticity. Theories that are available for wider classes of equations include discussions of Lie symmetries, improperly posed problems and integrable nonlinear equations. The main purpose of the book, however, is to address real situations. The range of applications presented to the reader is intended to help to make the developing studies of nonlinear mathematics more understandable.
Improperly posed problems for nonlinear partial differential equations,
K.A. Ames; symmetry in nonlinear mechanics, W.F. Ames; geometry of the
Melnikov vector, S.N. Chow and M. Yamashita; nonlinear equations, A.S. Fokas;
Hamiltonian structure and integrability, B. Fuchssteiner; symmetric chaos, G.
King and I. Steward; Backlund and reciprocal transformations - gauge
connections, B.G. Konopelchenko and C. Rogers; nonlinear reaction-diffusion
systems, R.H. Martin, Jr. and M. Pierre; Riccati-type pseudopotentials and
their applications, M.C. Nucci; nonlinear elasticity - incremental equations
and bifurcation phenomena, R.W. Ogden.
