Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2000-01-10
Nonlinear Sciences
Exactly Solvable and Integrable Systems
24 pages
Scientific paper
We propose a nonlinear $\sigma$-model in a curved space as a general integrable elliptic model. We construct its exact solutions and obtain energy estimates near the critical point. We consider the Pohlmeyer transformation in Euclidean space and investigate the gauge equivalence conditions for a broad class of elliptic equations. We develop the inverse scattering transform method for the $\sinh$-Gordon equation and evaluate its exact and asymptotic solutions.
Gutshabash Sh. E.
Lipovskii V. D.
Nikulichev S. S.
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