\documentclass{standalone}
\usepackage{tikz}
\usepackage{mathtools}


\begin{document}
\begin{tikzpicture}
\\begin{tikzpicture}[scale=.75]
\fill[fill=lime] (5.5,0)--(0,0)--(5.5,5.5)..controls (5,3) and (6,3).. (5.5,0) ;

\fill[fill=cyan!20] (5.5,5.5)--(0,5.5)--(0,0);


\fill[fill=yellow] (0,5.5)--(-4.5,5.5)--(0,0);



\draw[thin,->] (-4.7,0)--(5.7,0) node[below]{$x$};
\draw[thin,->] (0,0)--(0,5.7) node[left]{$t$};

\draw (0,0)--(5.5,5.5);
 \draw (0,0)--(-4.5,5.5);
 
\node[rotate=45] at (2.6,2.3)  {$x=c_1t$};
\node[right] at (.5,.4) {$u=\phi (t+c_1^{-1} x)$}; 

\node[right] at (.1,4.4) {$\begin{aligned}u=&\phi (t+c_1^{-1} x)\\ 
+&\psi (t-c_1^{-1} x)\end{aligned}$}; 

\node[left] at (-.1,5) {$u=\chi(t + c_2^{-1} x)$}; 

\node[rotate=-52] at (-2.2,2.3)  {$x=-c_2t$};

\end{tikzpicture}
\end{document}