# leto/thesis

fix typos for publication

git-svn-id: svn+ssh://leto.net/usr/local/svn/thesis@152 c868c573-c6a3-dc11-90ff-0002b3153201
1 parent 73f4f0d commit a1ebb329796cf73db60ecd5bcea2ff43b5e528a4 leto committed May 12, 2008
Showing with 4 additions and 4 deletions.
1. GPC/GPC.pdf
2. GPC/GPC.ps
3. +1 −1 GPC/section3.tex
4. +3 −3 GPC/section4.tex
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 @@ -187,7 +187,7 @@ \subsection{ Near $C_0$ } \begin{subequations} \begin{eqnarray} k &=& \sqrt{\frac{-\epsilon}{4q}} \label{eq:keq} \\ -\ell &=& \frac{ - 3 \epsilon c^2 }{2 q \left(3 a_3 + 5 a_5\right) } +\ell &=& \frac{ - 9 \epsilon c^2 }{2 q \left(3 a_3 + 5 a_5\right) } \end{eqnarray} \end{subequations}
 @@ -84,7 +84,7 @@ \section{Normal form near $C_1$: possible solitary wave solutions} \begin{eqnarray} \mathcal{O}(A^2): & b_* \zeta_1 &= L_{0q} \Psi_{2000}^0 - G_{1,2}(\zeta_0,\zeta_0) \\ \mathcal{O}(\left|C\right|^2):& c_* \zeta_1 &= L_{0q} \Psi_{0011}^0 -2 G_{1,2}(\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 - G_{1,2}(\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 G_{1,2}(\zeta_0,\zeta_+) \label{eq:AC} \end{eqnarray} \end{subequations} @@ -123,15 +123,15 @@ \section{Normal form near $C_1$: possible solitary wave solutions} \begin{subequations}\label{eq:GPC1normal} \begin{eqnarray} \label{eq:GPC1normalA} \frac{dA}{dz} &=& B \\ -\frac{dB}{dz} &=& -\frac{\epsilon}{q} A - b_* A^2 + \frac{1}{c^2}\left( \frac{7}{2 \sqrt{-q} } a_3 - \frac{i}{3} a_2 \right) \left|C\right|^2 \label{eq:GPC1normalB} \\ +\frac{dB}{dz} &=& -\frac{\epsilon}{q} A - \frac{a_3}{c^2} A^2 + \frac{1}{c^2}\left( \frac{7}{2 \sqrt{-q} } a_3 - \frac{i}{3} a_2 \right) \left|C\right|^2 \label{eq:GPC1normalB} \\ \frac{dC}{dz} &=& i \sqrt{-q} C - i \frac{\sqrt{-q} }{q^3} C\epsilon + i \frac{1}{c^2}\left( \frac{7}{2 \sqrt{-q} } a_3 - \frac{i}{3} a_2 \right)A C \label{eq:GPC1normalC} \end{eqnarray} \end{subequations} for \eqref{eq:GPC1} and \begin{subequations}\label{eq:GPC2normal} \begin{eqnarray} \label{eq:GPC2normalA} \frac{dA}{dz} &=& B \\ -\frac{dB}{dz} &=& -\frac{\epsilon}{q} A - b_* A^2 + \frac{1}{c^2}\left( 16 a_3 + \frac{140}{3} a_5 \right) \left|C\right|^2 \label{eq:GPC2normalB} \\ +\frac{dB}{dz} &=& -\frac{\epsilon}{q} A - \frac{3a_3+5a_5}{3c^2} A^2 + \frac{1}{c^2}\left( 16 a_3 + \frac{140}{3} a_5 \right) \left|C\right|^2 \label{eq:GPC2normalB} \\ \frac{dC}{dz} &=& i \sqrt{-q} C - i \frac{\sqrt{-q} }{q^3} C\epsilon + i \frac{1}{\sqrt{-q} c^2}\left( \frac{7}{2 } a_3 + \frac{32}{3} a_5 \right)A C \label{eq:GPC2normalC} \end{eqnarray} \end{subequations}