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 The Ishimori equation 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 Ishimori equation is the Davey-Stewartson equation.

See also

Nonlinear Schrödinger equation Heisenberg model (classical) Spin wave Landau–Lifshitz model Soliton Vortex Nonlinear systems Davey–Stewartson equation

References

External links Ishimori_system at the dispersive equations wiki