 Home

Codex Wiki

Physics

Branch of physics

Integrable systems

Lax pair

Isospectral Lax equation

If
$$
\dot L=[L,A],
$$
then every positive power has constant trace:
$$
\frac d{dt}\operatorname{tr}(L^n)
=n\operatorname{tr}(L^{n-1}[A,L])=0.
$$
The final equality is the cyclic property of the <matrix trace>.

Trace invariants of a Lax equation

Past exam of the mathematics course of the University of Cambridge / 2005 / iii / Paper 56 / 3 / Solution

Past exam of the mathematics course of the University of Cambridge / 2020 / ii / Paper 1 / 33C / b / iv / Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 1 / 33D / c / Solution

Zero-diagonal Jacobi Lax pair for the finite Volterra lattice

Trace invariants of a Lax equation

 Ancestors (6)

 Incoming links (4)

 Discussion (0)

 Articles by others on the same topic (0)

Trace invariants of a Lax equation

 Ancestors (6)

 Incoming links (4)

 Discussion (0)  Subscribe (1)

 Articles by others on the same topic (0)

 Discussion (0)