diff --git a/benchmarks/solitary_wave/doc/solitary_wave.md b/benchmarks/solitary_wave/doc/solitary_wave.md
index bc95a0b6942..2836f2c618d 100644
--- a/benchmarks/solitary_wave/doc/solitary_wave.md
+++ b/benchmarks/solitary_wave/doc/solitary_wave.md
@@ -57,7 +57,13 @@ This is only valid in the limit of small porosity $\phi_0 \ll 1$.
```{figure-md} fig:setup-solitary-wave
-Setup of the solitary wave benchmark. The domain is 400 m high and includes a low porosity (ϕ = 0.001) background with an initial perturbation (ϕ = 0.1). The solid density is 3300 kg/m3 and the melt density is 2500 kg/m3. We apply the negative phase speed of the solitary wave us = − c ez as velocity boundary condition, so that the wave will stay at its original position while the background is moving.
+Setup of the solitary wave benchmark. The domain is 400 m high and
+includes a low porosity ($\phi = 0.001$) background with an initial
+perturbation ($\phi = 0.1$). The solid density is 3300 kg/m$^3$ and
+the melt density is 2500 kg/m$^3$. We apply the negative phase speed of
+the solitary wave $ u_s = -c e_z$ as velocity boundary condition, so
+that the wave will stay at its original position while the background
+is moving.
```
The parameter file and material model for this setup can be found in
diff --git a/cookbooks/burnman/doc/burnman.md b/cookbooks/burnman/doc/burnman.md
index 5b4e733415e..2645e87f960 100644
--- a/cookbooks/burnman/doc/burnman.md
+++ b/cookbooks/burnman/doc/burnman.md
@@ -67,9 +67,9 @@ Visualizing material properties such as density, thermal expansivity or specific
We can also visualize the gravity and the adiabatic profile, to ensure that the data we provided in the `data/adiabatic-conditions/ascii-data/isentrope_properties.txt` file is used in our model.
```{figure-md} fig:burnman-convection
-
+
-Compressible convection in a 2d spherical shell, using a reference profile exported form BurnMan, which is based on the Birch-Murnaghan equation of state. The figure shows the state at the end of the model evolution over 260 Ma.
+Compressible convection in a 2d spherical shell, using a reference profile exported from BurnMan, which is based on the Birch-Murnaghan equation of state. The figure shows the state at the end of the model evolution over 260 Ma.
```
@@ -99,7 +99,7 @@ They demonstrate that upwellings and downwellings may occur in slightly differen
```{figure-md} fig:burnman-comparison
-Comparison between the anelastic liquid approximation, the truncated anelastic liquid approximation and the isothermal compression approximation, showing the temperature distribution for the different models at the end of the model evolution at 260 Ma.
+Comparison between the anelastic liquid approximation, the truncated anelastic liquid approximation and the isothermal compression approximation, showing the temperature distribution for the different models at the end of the model evolution at 260 Ma.
```
```{figure-md} fig:burnman-vrms