Invariants of fast solutions of KdV-Burgers Equations

which is obtained from eq. (1) by replacing Uk with A 2 k and rescaling t, while the cyclic boundary condition case is discussed in Goodman & Lax [2] for even N . Moser notes the existence of dN/2e polynomials of Ak that are invariant and states that they are independent. They are the coefficients of the characteristic equation of an N + 1 by N + 1 zero-diagonal symmetric Jacobi matrix whose terms depend on the Ak. Goodman & Lax discuss N/2 invariants expressed as the traces of powers of an N by N zero-diagonal symmetric Jacobi matrix and mention an additional invariant and this has recently been discussed in [1]. Here we give an explicit form of the invariants in both cases (including the cyclic case for odd N), show that this form is equivalent to the forms in the cited work, and show that they are functionally independent.