Noncom

The main characteristics of the real-world decision-making problems facing humans today are multidimensional and have multiple objectives including eco­ nomic, environmental, social, and technical ones. Hence, it seems natural that the consideration of many objectives in the actual decision-making process re­ quires multiobjective approaches rather than single-objective. One ofthe major systems-analytic multiobjective approaches to decision-making under constraints is multiobjective optimization as a generalization of traditional single-objective optimization. Although multiobjective optimization problems differ from single­ objective optimization problems only in the plurality of objective functions, it is significant to realize that multiple objectives are often noncom mensurable and conflict with each other in multiobjective optimization problems.

This book presents a development of invariant manifold theory for a spe­ cific canonical nonlinear wave system -the perturbed nonlinear Schrooinger equation. The main results fall into two parts. The first part is concerned with the persistence and smoothness of locally invariant manifolds. The sec­ ond part is concerned with fibrations of the stable and unstable manifolds of inflowing and overflowing invariant manifolds.

This book presents a development of invariant manifold theory for a spe­ cific canonical nonlinear wave system -the perturbed nonlinear Schrooinger equation. The main results fall into two parts. The first part is concerned with the persistence and smoothness of locally invariant manifolds. The sec­ ond part is concerned with fibrations of the stable and unstable manifolds of inflowing and overflowing invariant manifolds.

This book presents a development of invariant manifold theory for a spe­ cific canonical nonlinear wave system -the perturbed nonlinear Schrooinger equation. The main results fall into two parts. The first part is concerned with the persistence and smoothness of locally invariant manifolds. The sec­ ond part is concerned with fibrations of the stable and unstable manifolds of inflowing and overflowing invariant manifolds.

This book presents a development of invariant manifold theory for a spe­ cific canonical nonlinear wave system -the perturbed nonlinear Schrooinger equation. The main results fall into two parts. The first part is concerned with the persistence and smoothness of locally invariant manifolds. The sec­ ond part is concerned with fibrations of the stable and unstable manifolds of inflowing and overflowing invariant manifolds.