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29 ucf_thesis/abstract.tex
@@ -16,22 +16,19 @@ \chapter*{ABSTRACT}
\item a generalized microstructure PDE.
\end{itemize}
-Limited analytic results exist for the occurrence of one family
-of solitary wave solutions for each of these equations. Since, as
-mentioned above, solitary wave solutions often play a central role in
-the long-time evolution of an initial disturbance, we consider
-such solutions of both models here (via the normal form approach)
-within the framework of reversible systems theory.
-
-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.
-For both models, the new family of solutions occur in regions of
-parameter space distinct from the known solitary wave solutions and
-are thus entirely new.
+Limited analytic results exist for the occurrence of one family of solitary
+wave solutions for each of these equations. Since, as mentioned above, solitary
+wave solutions often play a central role in the long-time evolution of an
+initial disturbance, we consider such solutions of both models here (via the
+normal form approach) within the framework of reversible systems theory.
+
+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. For the
+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.

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