The Augment method appends some DEs des to the LHPDE object obj.

The method returns a new LHPDE object with new conditions des appended.

The returned LHPDE object can be in rif-reduced form (see DEtools[rifsimp]) by specifying rifReduce = true.

This method is associated with the LHPDE object. For more detail, see Overview of the LHPDE object.

$\mathrm{with}\left(\mathrm{LieAlgebrasOfVectorFields}\right)\:$

$\mathrm{Typesetting}:-\mathrm{Settings}\left(\mathrm{userep}\=\mathrm{true}\right)\:$

$\mathrm{Typesetting}:-\mathrm{Suppress}\left(\left\{\mathrm{\ξ}\,\mathrm{\η}\right\}\left(x\,y\right)\right)$

$S≔\mathrm{LHPDE}\left(\left[\frac{{\partial }^2}{\partial y^2}\mathrm{\ξ}\left(x\,y\right)\=0\,\frac{\partial }{\partial x}\mathrm{\η}\left(x\,y\right)\=-\left(\frac{\partial }{\partial y}\mathrm{\ξ}\left(x\,y\right)\right)\,\frac{\partial }{\partial y}\mathrm{\η}\left(x\,y\right)\=0\,\frac{\partial }{\partial x}\mathrm{\ξ}\left(x\,y\right)\=0\right]\,\mathrm{indep}\=\left[x\,y\right]\,\mathrm{dep}\=\left[\mathrm{\ξ}\,\mathrm{\η}\right]\right)$

$S≔\left[{\mathrm{\xi }}_{y,y}=0\,{\mathrm{\eta }}_x=-{\mathrm{\xi }}_y\,{\mathrm{\eta }}_y=0\,{\mathrm{\xi }}_x=0\right],\mathrm{indep}=\left[x\,y\right],\mathrm{dep}=\left[\mathrm{\xi }\,\mathrm{\eta }\right]$

$\mathrm{Augment}\left(S\,\left[\frac{\partial }{\partial y}\mathrm{\ξ}\left(x\,y\right)\=0\right]\right)$

$\left[{\mathrm{\xi }}_{y,y}=0\,{\mathrm{\eta }}_x=-{\mathrm{\xi }}_y\,{\mathrm{\eta }}_y=0\,{\mathrm{\xi }}_x=0\,{\mathrm{\xi }}_y=0\right],\mathrm{indep}=\left[x\,y\right],\mathrm{dep}=\left[\mathrm{\xi }\,\mathrm{\eta }\right]$

$\mathrm{Augment}\left(S\,\left[\frac{\partial }{\partial y}\mathrm{\ξ}\left(x\,y\right)\=0\right]\,\mathrm{rifReduce}\=\mathrm{true}\right)$

$\left[{\mathrm{\xi }}_x=0\,{\mathrm{\eta }}_x=0\,{\mathrm{\xi }}_y=0\,{\mathrm{\eta }}_y=0\right],\mathrm{indep}=\left[x\,y\right],\mathrm{dep}=\left[\mathrm{\xi }\,\mathrm{\eta }\right]$

The Augment command was introduced in Maple 2020.

For more information on Maple 2020 changes, see Updates in Maple 2020.