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Nonlocal \({\bar \partial}\)-problem and \((2+1)\)-dimensional soliton equations. (English) Zbl 0682.35092

Plasma theory and nonlinear and turbulent processes in physics, Proc. Int. Workshop, Kiev/USSR 1987, 7-19 (1988).
Summary: [For the entire collection see Zbl 0644.00031.]
A method of constructing \((2+1)\)-dimensional nonlinear integrable equations and their solutions by means of the nonlocal \({\bar \partial}\)- problem is developed. Using different normalizations of the nonlocal \({\bar \partial}\)-problem the basic set of equations is obtained; the Lagrangian of this set is found. Other integrable equations are degenerate cases of the basic set of equations; they are also Lagrangian.

MSC:

35Q99 Partial differential equations of mathematical physics and other areas of application

Citations:

Zbl 0644.00031