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...ne equation to solutions of another equation. Usually one only works with transforms which are given explicitly by an algebraic formula. A list of transforms [[:Category:Transforms|can be found here]].

The Lorentz transforms are the linear isometries of [[Minkowski spacetime]]. [[Category:transforms]]

== Equations in which gauge transforms arise == [[Category:transforms]]

...g case, the ''Miura transformation'' <math> v = \partial_x u + u^2 </math> transforms a solution of defocussing [[mKdV]] to a solution of [[KdV]] ...se, the Miura transform is now <math>v = \partial_x u + i u^2</math>. This transforms <span class="SpellE">focussing</span> mKdV to ''complex-valued'' KdV, which

The method of '''normal forms''' transforms the Hamiltonian of an equation via a canonical transformation to remove (or [[Category:Transforms]]

[[Category:transforms]]

...l operations such as Hilbert transforms, Hartree-type potentials, or Riesz transforms. Such equations arise as various approximations to wave equations, see e.g

[[Category:Transforms]]

...erators, then generalizations of the Fourier transform (such as scattering transforms or Fourier integral operators) can be employed.

[[Category:Transforms]]

[[Category:Transforms]]

[[Category:Transforms]]

...uite different but one can still use derivative NLS techniques (i.e. gauge transforms and energy methods) to obtain some local existence results [[LiPo1993]]. F

...appens? Do there exist finite time blowup solutions? This problem is gauge transforms into quintic focusing NLS on <math>\mathbb{R}</math> which is known to have

...over YM that the Coulomb gauge is easily constructed globally using Riesz transforms, so there are less technical issues involved with this gauge.