nLab
Lax equation
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
Last revised on October 15, 2012 at 21:47:23.
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