Abstract
A necessary and sufficient condition is established for the existence of a $1 - 1$ transformation of a system of nonlinear differential equations to a system of linear equations. The obtained theorems enable one to construct such transformations from the invariance groups of differential equations. The hodograph transformation, the Legendre transformation and Lie’s transformation of the Monge–Ampére equation are shown to be special cases. Noninvertible transformations are also considered. Examples include Burgers’ equation, a nonlinear diffusion equation and the Liouville equation.
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