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git-svn-id: svn+ssh://leto.net/usr/local/svn/thesis@143 c868c573-c6a3-dc11-90ff-0002b3153201
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commit de63a8e79c990d22d0f0d1103e7cc09ff6e9505a 1 parent 1aae05b
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  1. +5 −3 ucf_thesis/chapter_4.tex
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8 ucf_thesis/chapter_4.tex
@@ -42,9 +42,11 @@ \chapter{CHAPTER FOUR: RESULTS} \label{chapter_4}
One may easily verify that $\lim_{z\rightarrow\pm\infty} A(z) = 0$, therefore
$A(z)$ compromises a homoclinic orbit, since it connects the fixed point $0$ to
itself. The importance of homoclinic orbits in the traveling wave ODE is that
-they correspond to soliton pulse solutions of the original PDE \cite{IA}.
-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
+they correspond to soliton pulse solutions of the original PDE \cite{IA}. Iooss
+\& P\'erou\`eme have proved that solutions in the traveling wave ODE persist in
+the original system \cite{IP} for reversible 1:1 resonance vector fields. 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.
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