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minor formatting and wordplay

git-svn-id: svn+ssh://leto.net/usr/local/svn/thesis@141 c868c573-c6a3-dc11-90ff-0002b3153201
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  1. +10 −12 ucf_thesis/chapter_1.tex
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22 ucf_thesis/chapter_1.tex
@@ -77,18 +77,16 @@ \chapter{CHAPTER ONE: INTRODUCTION} \label{chapter_1}
Besides confirming the existence of the known family of solitary waves for each
model, we find a continuum of delocalized solitary waves (or homoclinics to
small-amplitude periodic orbits). On isolated curves in the relevant parameter
-region, the delocalized waves reduce to genuine embedded solitons. These curves
-are determined from the regions of different eigenvalue configurations in the
-characteristic equation of the traveling wave ODE. An example of this
-would be an eigenvalue of multiplicity two splitting into two simple eigenvalues,
-or two simple eigenvalues coalescing into an eigenvalue of multiplicity two
-as a parameter is varied.
+region, known as transition curves, the delocalized waves reduce to genuine
+embedded solitons. These curves are determined from the regions of different
+eigenvalue configurations in the characteristic equation of the traveling wave
+ODE. An example of a change in configuration would be an eigenvalue of
+multiplicity two splitting into two simple eigenvalues, or two simple
+eigenvalues coalescing into an eigenvalue of multiplicity two as a parameter is
+varied.
For the generalized Microstructure equation, the new family of solutions occur
in regions of parameter space distinct from the known solitary wave solutions
-and are thus entirely new.
-
-Directions for future work, including the dynamics of each family of
-solitary waves using exponential asymptotics techniques, are also mentioned.
-
-
+and are thus entirely new. Directions for future work, including the dynamics of
+each family of solitary waves using exponential asymptotics techniques, are also
+mentioned.
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