The DChange method performs change of variables tr in the LHPDE object obj.

The method returns a new LHPDE object written with respect to new dependent and independent variables that are on the right hand side of tr.

The new dependent and independent variables can also be fully specified via the optional arguments indep = ivars and dep = dvars.

The returned LHPDE object can be rif-reduced if the option rifReduce = true is specified.

The method name dchange is provided as alias.

This DChange method is based on the existing Maple function PDEtools[dchange].

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

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

$S≔\mathrm{LHPDE}\left(\left[\mathrm{diff}\left(u\left(x\,y\right)\,x\right)+\mathrm{diff}\left(u\left(x\,y\right)\,y\right)=0\right]\right)$

$S≔\left[\frac{\partial }{\partial x}u\left(x\,y\right)+\frac{\partial }{\partial y}u\left(x\,y\right)=0\right],\mathrm{indep}=\left[x\,y\right],\mathrm{dep}=\left[u\left(x\,y\right)\right]$

$\mathrm{DChange}\left(\left\{x=r+s\,y=r-s\,u\left(x\,y\right)=v\left(r\,s\right)\right\}\,S\right)$

$\left[\frac{\partial }{\partial r}v\left(r\,s\right)=0\right],\mathrm{indep}=\left[r\,s\right],\mathrm{dep}=\left[v\left(r\,s\right)\right]$

$S≔\mathrm{LHPDE}\left(\left[\mathrm{diff}\left(u\left(x\right)\,x\right)+a\left(x\right)u\left(x\right)=0\right]\,\mathrm{dep}=\left[u\left(x\right)\right]\right)$

$S≔\left[\frac{\ⅆ}{\ⅆx}u\left(x\right)+a\left(x\right)u\left(x\right)=0\right],\mathrm{indep}=\left[x\right],\mathrm{dep}=\left[u\left(x\right)\right]$

$\mathrm{DChange}\left(\left\{x=t\,u\left(x\right)=\mathrm{diff}\left(v\left(t\right)\,t\right)\right\}\,S\,\mathrm{dep}=\left[v\left(t\right)\right]\right)$

$\left[\frac{{\ⅆ}^2}{\ⅆt^2}v\left(t\right)+a\left(t\right)\left(\frac{\ⅆ}{\ⅆt}v\left(t\right)\right)=0\right],\mathrm{indep}=\left[t\right],\mathrm{dep}=\left[v\left(t\right)\right]$

$\mathrm{Sp}≔\mathrm{DChange}\left(\left\{x=t\,u\left(x\right)=\mathrm{diff}\left(v\left(t\right)\,t\right)\right\}\,S\,\mathrm{dep}=\left[v\left(t\right)\right]\,\mathrm{rifReduce}=\mathrm{true}\right)$

$\mathrm{Sp}≔\left[\frac{{\ⅆ}^2}{\ⅆt^2}v\left(t\right)=-a\left(t\right)\left(\frac{\ⅆ}{\ⅆt}v\left(t\right)\right)\right],\mathrm{indep}=\left[t\right],\mathrm{dep}=\left[v\left(t\right)\right]$

$\mathrm{IsRifReduced}\left(\mathrm{Sp}\right)$

$\mathrm{true}$

$S≔\mathrm{LHPDE}\left(\left[\right]\,\mathrm{dep}=\left[u\left(x\,y\right)\,v\left(x\,y\right)\right]\right)$

$S≔\left[\right],\mathrm{indep}=\left[x\,y\right],\mathrm{dep}=\left[u\left(x\,y\right)\,v\left(x\,y\right)\right]$

$\mathrm{DChange}\left(\left\{x=s\,y=t\,u\left(x\,y\right)=\mathrm{\phi }\left(s\,t\right)\right\}\,S\,\mathrm{dep}=\left[\mathrm{\phi }\left(s\,t\right)\,v\left(s\,t\right)\,\mathrm{\delta }\left(s\,t\right)\right]\right)$

$\left[\right],\mathrm{indep}=\left[s\,t\right],\mathrm{dep}=\left[\mathrm{\phi }\left(s\,t\right)\,v\left(s\,t\right)\,\mathrm{\delta }\left(s\,t\right)\right]$

The DChange command was introduced in Maple 2020.

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