DChange - Maple Help

DChange

change coordinates in a LAVF object

 Calling Sequence DChange( tr, obj, vf, options ) dchange( tr, obj, vf, options )

Parameters

 tr - set of equations corresponding to the transformation from the old variables on the left-hand side of the equations to the new variables on the right-hand side obj - a LAVF object vf - a VectorField object options - optional arguments that will be passed down to PDEtools[dchange] command

Description

 • The DChange method performs change of variables tr in the LAVF object obj.
 • The method returns a new LAVF object written with respect to independent variables and the dependent variables specified in vf
 • The vf argument is required.  Other options are as for PDEtools:-dchange, and are ultimately passed through to it.
 • The name dchange is provided as an alias.
 • This method is associated with the LAVF object. For more detail see Overview of the LAVF object.

Examples

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

Build a LAVF for the sl[2] action on the line...

 > $X≔\mathrm{VectorField}\left(\left[\left[\mathrm{\xi }\left(x\right),x\right]\right]\right)$
 ${X}{≔}{\mathrm{\xi }}{}\left({x}\right){}\frac{{\partial }}{{\partial }{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}$ (1)
 > $\mathrm{Sys}≔\mathrm{LHPDE}\left(\left[\mathrm{diff}\left(\mathrm{\xi }\left(x\right),x,x,x\right)=0\right],\mathrm{indep}=\left[x\right],\mathrm{dep}=\left[\mathrm{\xi }\right]\right)$
 ${\mathrm{Sys}}{≔}\left[\frac{{{ⅆ}}^{{3}}}{{ⅆ}{{x}}^{{3}}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{\xi }}{}\left({x}\right){=}{0}\right]{,}{\mathrm{indep}}{=}\left[{x}\right]{,}{\mathrm{dep}}{=}\left[{\mathrm{\xi }}{}\left({x}\right)\right]$ (2)
 > $L≔\mathrm{LAVF}\left(X,\mathrm{Sys}\right)$
 ${L}{≔}\left[{\mathrm{\xi }}{}\left({x}\right){}\frac{{\partial }}{{\partial }{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}\right]\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{&where}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\left\{\left[\frac{{{ⅆ}}^{{3}}}{{ⅆ}{{x}}^{{3}}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{\xi }}{}\left({x}\right){=}{0}\right]\right\}$ (3)

Now set up another vector field with a change of variables...

 > $Y≔\mathrm{VectorField}\left(\left[\left[\mathrm{\eta }\left(y\right),y\right]\right]\right)$
 ${Y}{≔}{\mathrm{\eta }}{}\left({y}\right){}\frac{{\partial }}{{\partial }{y}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}$ (4)
 > $\mathrm{DChange}\left(\left\{x=y\right\},L,Y\right)$
 $\left[{\mathrm{\eta }}{}\left({y}\right){}\frac{{\partial }}{{\partial }{y}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}\right]\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{&where}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\left\{\left[\frac{{{ⅆ}}^{{3}}}{{ⅆ}{{y}}^{{3}}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{\eta }}{}\left({y}\right){=}{0}\right]\right\}$ (5)

Compatibility

 • The DChange command was introduced in Maple 2020.