Normal form

The method of normal forms transforms the Hamiltonian of an equation via a canonical transformation to remove (or attenuate) non-resonant portions of the nonlinearity, replacing them with more tractable terms. For instance, normal forms can replace a quadratic nonlinearity with a cubic one. They are particularly useful in nonlinear wave equations.

In Bo-p2 the method of normal forms was shown to be compatible with the I-method, and used to improve the low-regularity global regularity theory for certain nonlinear Schrodinger equations.

Normal forms should not be confused with the unrelated concept of a null form. They achieve a similar effect as gauge transformations, although the latter arise from the differential geometry of connections and bundles rather than from the structure of the Hamiltonian.