Symmetries and soliton solutions of nonlinear equations
One of the popular ways to construct a family of soliton-type solutions of a system of partial differential equations is to derive both the family and the system from the same source. This is exactly what is done in the paper. Let g be a 2-parameter family of finite-dimensional representations of a Lie group (x,y-parameters), and \[ (\partial g/\partial x)| g=U(x,y);\quad (\partial g/\partial y)| g=V(x,y). \] Then from Cartan-Maurer equation \[ \partial U/\partial y-\partial V/\partial x- [U,V]=0 \] one derives a system of p.d.e. Explicit formulae are given for soliton solutions of the system, which originate from the same Cartan- Maurer equation.
scientific article; zbMATH DE number 3935550
scientific article