论文信息 - On the geometric origin of the equation ϕ,11 — ϕ,22 = eϕ

On the geometric origin of the equation ϕ,11 — ϕ,22 = eϕ — e-2ϕ

It is shown that the equation ϕ,11 — ϕ,22 = eϕ — e-2ϕ determines the intrinsic geometry of the two-dimensional affine sphere in the three-dimensional unimodular affine space like the sine-Gordon equation describes the metric on the surface of a constant negative curvature in the three-dimensional Euclidean space. The linear equations that determine the moving frame on the affine sphere are the Lax operators to the equation ϕ,11 — ϕ,22 = eϕ — e-2ϕ.

V. V. Nesterenko

[1] V. Korepin,et al. Quantum theory of solitons , 1978 .

[2] T. Regge,et al. Unified Approach to Strings and Vortices with Soliton Solutions , 1976 .

[3] N. Papanicolaou,et al. Integrability of the classical $[\overline \psi_{i}\psi_{i}]^{2}_{2}$ and $[\overline \psi_{i}\psi_{i}]^{2}_{2}- [\overline \psi_{i}\gamma_{5}\psi_{i}]^{2}_{2}$ interactions , 1978 .

[4] J. A. Todd,et al. An Introduction to Differential Geometry with Use of the Tensor Calculus , 1941, The Mathematical Gazette.

[5] A. Zamolodchikov,et al. Quantum S-matrix of the (1 + 1)-dimensional Todd chain , 1979 .

[6] A. Perelomov,et al. Two-dimensional generalized Toda lattice , 1981 .

[7] B. Barbashov,et al. Differential Geometry and Nonlinear Field Models , 1980, 1980.

[8] V. Canuto,et al. The cosmological constant, broken gauge theories and 3 K black-body radiation , 1977 .

[9] T. J. Willmore,et al. Cours de géométrie différentielle locale , 1959 .

[10] R. Sasaki. Geometrization of soliton equations , 1979 .

[11] K. Pohlmeyer,et al. Integrable Hamiltonian systems and interactions through quadratic constraints , 1976 .

[12] R. K. Dodd,et al. Polynomial conserved densities for the sine-Gordon equations , 1977, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.