This article is cited in 6 papers

An integrable class of differential equations with nonlocal nonlinearity on Lie groups

M. M. Goncharovskiy, I. V. Shirokov

Omsk State University for Technology, Omsk, Russia

Abstract: We construct the general and $N$-soliton solutions of an integro-differential Schrödinger equation with a nonlocal nonlinearity. We consider integrable nonlinear integro-differential equations on the manifold of an arbitrary connected unimodular Lie group. To reduce the equations on the group to equations with a smaller number of independent variables, we use the method of orbits in the coadjoint representation and the generalized harmonic analysis based on it. We demonstrate the capacities of the algorithm with the example of the $SO(3)$ group.

Keywords: nonlinear integro-differential equation, soliton, Lie group, coadjoint representation, harmonic analysis.

Received: 01.03.2009

DOI: 10.4213/tmf6445

 English version: Theoretical and Mathematical Physics, 2009, 161:3, 1604–1615

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