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diff --git a/MS/section2.tex b/MS/section2.tex
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--- a/MS/section2.tex
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@@ -8,7 +8,6 @@ \section{Solitary waves; local bifurcations}
 \end{equation}
 
 where 
-% the notation $\mathcal{N[\phi]}$ means that the operator $\mathcal{N}$ operates on $\phi$ and all of it's derivatives, and 
 \begin{equation}
 \mathcal{N}\left[\phi\right] = -\Delta_1 \phi_z^2 - b \Delta_1 \phi \phi_{zz}
 \end{equation}
diff --git a/MS/section4.tex b/MS/section4.tex
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--- a/MS/section4.tex
+++ b/MS/section4.tex
@@ -90,7 +90,7 @@ \section{Normal form near $C_1$: possible solitary wave solutions}
 \begin{eqnarray}
 \mathcal{O}(A^2): &		b_* \zeta_1 &= L_{0q} \Psi_{2000}^0 - F_2(\zeta_0,\zeta_0) \\
 \mathcal{O}(\left|C\right|^2):&	c_* \zeta_1 &= L_{0q} \Psi_{0011}^0 -2 F_2(\zeta_+,\zeta_-) \label{eq:cstar} \\
-\mathcal{O}(\epsilon C): &-\frac{i}{q} \left(d_1 \zeta_+ +  d_0 \Psi_{0010}^1\right) &= L_{0q} \Psi_{0010}^1 - F_2(\Psi_{0010}^1,\Psi_{0010}^1) \\
+\mathcal{O}(\epsilon C): &-\frac{i}{q} \left(d_1 \zeta_+ +  d_0 \Psi_{0010}^1\right) &= L_{0q} \Psi_{0010}^1 \\
 \mathcal{O}(A C): 	&i d_2 \zeta_+ + i d_0 \Psi_{1010}^0 &= L_{0q} \Psi_{1010}^0 - 2 F_2(\zeta_0,\zeta_+) \label{eq:AC}
 \end{eqnarray}
 \end{subequations}