Ishimori equation

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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).

Contents

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 (CCHFE). The CCHFE is integrable.

Equivalent counterpart

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

See also

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