Ishimori equation


The Ishimori equation is a partial differential equation proposed by the Japanese mathematician. Its interest is as the first example of a nonlinear spin-one field model in the plane that is integrable.

Equation

The Ishimori equation has the form

Lax representation

The Lax representation
of the equation is given by
Here
the are the Pauli matrices and is the identity matrix.

Reductions

IE admits an important reduction:
in 1+1 dimensions it reduces to the continuous classical Heisenberg ferromagnet equation. The CCHFE is integrable.

Equivalent counterpart

The equivalent counterpart of the IE is the Davey-Stewartson equation.