I would like to ask a question that I had asked a few days ago on the site math.stackexchange and I still have not received an answer.
If we have a Lax operator, we know that the spectrum of this operator is conserved over time.
Suppose that we have an equation that admits $L_u$ as a Lax operator, then can we say that all the conservation laws of this equation can be written in terms of the spectrum of $L_u$ ? Especially if $L_u$ has a discrete spectrum ?
Thanks in advance.
