## 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

Zbl 0644.00031