New multidimensional partially integrable generalization of S-integrable N-wave equation

Details New multidimensional partially integrable generalization of S-integrable N-wave equation New multidimensional partially integrable generalization of S-integrable N-wave equation

2006-12-21

arxiv.org/abs/nlin/0612048v4

Nonlinear Sciences

Exactly Solvable and Integrable Systems

38 pages

Scientific paper

10.1063/1.2759444

This paper develops a modification of the dressing method based on the inhomogeneous linear integral equation with integral operator having nonempty kernel. Method allows one to construct the systems of multidimensional Partial Differential Equations (PDEs) having the differential polynomial forms in any dimension n. Associated solution space is not full, although it is parametrized by a certain number of arbitrary functions of (n-1)-variables. We consider 4-dimensional generalization of the classical (2+1)-dimensional S-integrable N-wave equation as an example.

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