Villarroel, Javier The inverse problem for Ward’s system. (English) Zbl 0737.35055 Stud. Appl. Math. 83, No. 3, 211-222 (1990). 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 Cited in 1 ReviewCited in 6 Documents 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 Keywords:inverse scattering transform; soliton theory; local Riemann problem; instantons; Ward’s system PDFBibTeX XMLCite \textit{J. Villarroel}, Stud. Appl. Math. 83, No. 3, 211--222 (1990; Zbl 0737.35055) Full Text: DOI 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 [4] Manakov, Lett. Math. Phys. 5 pp 247– (1981) · doi:10.1007/BF00420705 [5] Gohberg, Uspekhi Mat. Nauk 13 pp 2– (1958) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.