The Ishimori equation (IE) is a partial differential equation proposed by the Japanese mathematician Ishimori (1984). Its interest is as the first example of a nonlinear spin-one field model in the plane that is integrable ( Sattinger, Tracy & Venakides 1991 , p. 78).
The Ishimori equation has the form
The Lax representation
of the equation is given by
the are the Pauli matrices and is the identity matrix.
IE admits an important reduction: in 1+1 dimensions it reduces to the continuous classical Heisenberg ferromagnet equation (CCHFE). The CCHFE is integrable.
The equivalent counterpart of the IE is the Davey-Stewartson equation.
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The purpose of this page is to provide supplementary materials for the ordinary least squares article, reducing the load of the main article with mathematics and improving its accessibility, while at the same time retaining the completeness of exposition.
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