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The inverse problem for Ward’s system. (English) Zbl 0737.35055

The inverse scattering method is used to study a generalization (due to R. Ward) to 2+1 dimensions of the well known sigma model. The appropriate spectral problem is found to be a local Riemann problem with allowance of poles. By assuming particular distributions of these poles we obtain different solutions of our system: the celebrated instantons and other new solutions of the model.
Reviewer: J.Villarroel

MSC:

35P25 Scattering theory for PDEs
58J72 Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds
35R30 Inverse problems for PDEs
35Q40 PDEs in connection with quantum mechanics
35Q51 Soliton equations
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References:

[1] Ward, J. Math. Phys. 29 pp 386– (1988) · Zbl 0644.58038 · doi:10.1063/1.528078
[2] Ablowitz, Stud. Appl. Math. 77 pp 37– (1987) · Zbl 0656.35130 · doi:10.1002/sapm198777137
[3] Beals, Sympos. Pure Math. 43 pp 45– (1985) · doi:10.1090/pspum/043/812283
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