Lax equation is used in integrable systems; namely some systems are equivalent to the Lax equation.
Lax equation is a linear ordinary differential equation of the form
for -matrix-valued function , where is also a matrix. The pair is also called a Lax pair.
The Lax equation is the compatibility condition for the system
where is a vector function which is an eigenvector for with eigenvalue . To see this make a derivative of and use the Leibniz rule.
- Peter Lax, Integrals of nonlinear equation of evolution and solitary waves, Commun. on Pure and Applied Mathematics 21:5, 467–490, 1968 doi
Revised on October 15, 2012 21:47:23
by Zoran Škoda