\begin{table}[h!]\label{tab1}
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\caption{بعضی از معادلات غیرخطی که جواب‌های دقیقی به فرم\eqref{l8}و\eqref{l9}دارند}
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 مراجع  & جواب      & معادله   \\ \hline
$ \cite{V.F.} $ &  $T=\varphi (x)+\psi (t);~~~~~$ $$T = (a/b)\ln u,$$ $$u= \varphi (x) + \psi (t)$$&  $\dfrac{\partial T}{\partial t}=a\dfrac{\partial ^{2}T}{\partial x^{2}}+b(\dfrac{\partial T}{\partial x})^{2}$  \\
 $ \cite{Samarskii, Barenblatt}$  &\centering $ T=\varphi (x) \psi (t)$  & $ \dfrac{\partial T}{\partial t}=a\dfrac{\partial}{\partial x}(T^{m}\dfrac{\partial T}{\partial x})$   \\
$ \cite{Samarskii, Ovsyanikov} $ &\centering $ T = \varphi (x) + \psi (t)$ & $\dfrac{\partial T}{\partial t} = a\dfrac{\partial}{\partial x}(e^{\lambda t}\dfrac{\partial T}{\partial x})$ \\
$ \cite{Samarskii, Dorodnitsyn}$ & \centering $ T = \varphi (x) \psi (t)$ & $ \dfrac{\partial T}{\partial t} = a\dfrac{\partial ^{2}T}{\partial x^{2}} + aT \ln T$ \\
$ \cite{Samarskii}$ & \centering $T = \varphi (x)\psi (t)$ & $ \dfrac{\partial T}{\partial t} = ax^{-n}\dfrac{\partial}{\partial x}(x^{n}\dfrac{\partial T}{\partial x}) + bT \ln T$ \\
$ \cite{Frank}$ & \centering$ T= -2 \ln u,~ u=\varphi (x) + \psi (y)$ & $\dfrac{\partial ^{2}T}{\partial x^{2}} + \dfrac{\partial ^{2}T}{\partial y^{2}} = ae^{T}$ \\
$ \cite{Solitons}$ & \centering $ T = 2 \ln \dfrac{1+u}{1-u},~ u = \varphi (x)\psi (y)$ & $\dfrac{\partial ^{2}T}{\partial x^{2}} + \dfrac{ \partial ^{2}T}{\partial y^{2}} = a\sinh  T$ \\
$ \cite{Solitons}$ &  \centering $ T = e^{u},~ u = \varphi (x) + \psi (y)$ & $ \dfrac{\partial ^{2}T}{\partial x^{2}} + \dfrac{\partial ^{2}T}{\partial y^{2}} = aT \ln T$ \\
$ \cite{Solitons}$ & \centering $ T = 4a\tan u,~ u = \varphi (x)\psi (y)$ & $ \dfrac{\partial ^{2}T}{\partial x^{2}} + \dfrac{\partial ^{2}T}{\partial y^{2}} = a\sin T$ \\
$ \cite{A. D}$ & \centering $ T = F(u),~ u = \varphi (x) + \psi (y)$ & $ \dfrac{\partial}{\partial x}(ax^{n}\dfrac{\partial T}{\partial x}) + \dfrac{\partial}{\partial y}(by^{m}\dfrac{\partial T}{\partial y}) = cT^{k}$ \\
$\cite{A. D}$ & \centering $ T= F(u),~ u = \varphi (x) + \psi (y)$ & $\dfrac{\partial}{\partial x}(ae^{\lambdax}\dfrac{\partial T}{\partial x}) + \dfrac{\partial}{\partial y}(be^{\beta y}\dfrac{ \partialT}{\partial y}) = ce^{\gamma T}$ \\
$\cite{A. D}$ & \centering $ T= F(u),~ u = \varphi (x) + \psi (y)$ &  $\dfrac{\partial}{\partial x}(ax^{n}\dfrac{\partial T}{\partial x}) + \dfrac{\partial}{\partial y}(be^{\beta y}\dfrac{ \partialT}{\partial y}) = ce^{\gamma T}$ \\
$\cite{A. D}$ & \centering $T = \varphi (x) \psi (y)$ &  $\dfrac{\partial}{\partial x}(aT{n}\dfrac{\partial T}{\partial x}) + \dfrac{\partial}{\partial y}(bT^{m}\dfrac{ \partialT}{\partial y}) = 0 $ \\
$\cite{V.F.}$ & \centering $ T = \varphi (x) + \psi (y)$ & $\dfrac{\partial}{\partial x}(ae^{\lambda T}\dfrac{\partial T}{\partial x}) + \dfrac{\partial}{\partial y}(be^{\beta T}\dfrac{\partial T}{\partial y}) = 0$ \\
$ \cite{V.F.}$ & \centering $ T = -2 \ln u,~ u=\varphi (x) + \psi (t)$ & $ \dfrac{\partial ^{2}T}{\partial t^{2}} = \dfrac{\partial ^{2}T}{\partial x^{2}} + ae^{T}$ \\
$ \cite{Solitons}$ & \centering $ T = 2 \ln \dfrac{1+u}{1-u},~u = \varphi (x)\psi (t)$ & $\dfrac{\partial ^{2}^{T}}{\partial t^{2}} = \dfrac{\partial ^{2}T}{\partial x^{2}} + a\sinh  T$ \\
$ \cite{Solitons}$ & \centering $ T = e^{u},~ u = \varphi (x) + \psi (t)$ & $\dfrac{\partial ^{2}^{T}}{\partial t^{2}} = \dfrac{\partial ^{2}T}{\partial x^{2}} + aT\ln  T$ \\
$ \cite{Solitons}$ & \centering $ T = 4a\tan u,~ u = \varphi (x)\psi (t) $ & $\dfrac{\partial ^{2}^{T}}{\partial t^{2}} = \dfrac{\partial ^{2}T}{\partial x^{2}} + a\sin T$ \\
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