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The Cauchy problem for the Ishimori equations. (English) Zbl 0763.35077

Summary: Y. Ishimori [Progr. Theor. Phys. 72. No. 1, 33-37 (1984)] derived a nonlinear wave equation which is a two-dimensional analogue of the classical isotropic spin-chain in ferromagnetism. In this paper we show that the Cauchy problem associated to this equation is well-posed in Sobolev spaces when initial spins are almost parallel.

MSC:

35Q40 PDEs in connection with quantum mechanics
35B35 Stability in context of PDEs
35Q55 NLS equations (nonlinear Schrödinger equations)
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
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References:

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