nLab Manakov-Zakharov-Ward model

Idea

An integrable field theory in 3 dimensions featuring solitons.

References

Original articles:

• S. V. Manakov, V. E. Zakharov: Three-dimensional model of relativistic-invariant field theory, integrable by the Inverse Scattering Transform, Lett. Math. Phys. 5 (1981) 247–253 [doi:10.1007/BF00420705]

• Richard S. Ward: Soliton solutions in an integrable chiral model in $2+1$ dimensions, J. Math. Phys. 29 (1988) 386–389 [doi:10.1063/1.528078]

• Richard S. Ward: Nontrivial scattering of localized solitons in a (2+1)-dimensional integrable system, Physics Letters A 208 3 (1995) 203-208 [doi:10.1016/0375-9601(95)00782-X]

See also:

• Christopher Anand: Ward’s Solitons, Geometry & Topology 1 (1997) 9-20 [pdf]

Realization as a limit of the M2-brane sigma-model:

• David Osten: The Manakov-Zakharov-Ward model as an integrable decoupling limit of the membrane [arXiv:2505.17184]

• David Osten: An integrable sector for the membrane, talk at CQTS (Nov 2025)