Finite-dimensional reductions of generalized dynamical Burgers system and their intensities (Q2782071)

For the generalized dynamical Burgers system NEWLINE\[NEWLINE\frac{du}{dt} = uu_x+u_{xx}+v_x, \qquad \frac{dv}{dt} = (uv)_x-v_{xx}, NEWLINE\]NEWLINE given on the smooth functional manifold \( M\subset C^\infty(\mathbb R/2\pi\mathbb Z;\mathbb R^2) \) finite-dimensional reductions of the Moser type are studied. For all dimensions \( N\in\mathbb Z_+ \) the corresponding Lax representations are constructed in explicit form.