DID YOU KNOW? DTIC has over 3.5 million final reports on DoD funded research, development, test, and evaluation activities available to our registered users. Click

HERE to register or log in.

# Accession Number:

## ADA165317

# Title:

## Normal Forms and Quadratic Nonlinear Klein-Gordon Equations,

# Descriptive Note:

# Corporate Author:

## NEW YORK UNIV NY COURANT INST OF MATHEMATICAL SCIENCES

# Report Date:

## 1985-01-01

# Pagination or Media Count:

##
12.0

# Abstract:

## In studying nonlinear wave equations, perturbation techniques have proved to be extremely useful. We usually compare solutions of the nonlinear perturbed problem to solutions of the linear unperturbed problem. However, when we are interested in the asymptotic behavior of solutions of perturbed problems we have to restrict the class of nonlinearities f usually the degree, and we have to use a detailed analysis of solutions of the linear problem. An example of this is the fact that solving the nonlinear Klein-Gordon equation in 3 1 dimensions requires f to be at least of order 3. However, most physical models such as the relativistic superconductor model involve quadratic terms. Consequently the asymptotic behavior or even global existence of small solutions does not yield to direct perturbation techniques. One way of trying to avoid this problem is to try to transform the given nonlinear problem into another nonlinear problem which will yield to direct perturbation techniques. This procedure is very useful in the theory of ordinary differential equations and is called Poincares theory of normal forms. Reprints

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#