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The operator <math display="inline">M</math> describes how the eigenfunctions evolve over time, and generates a new eigenfunction <math display="inline">\widetilde{\psi} </math> of operator <math display="inline">L</math> from eigenfunction <math display="inline">\psi</math> of <math display="inline">L</math>.{{sfn|Aktosun|2009}}{{rp|4963}}
: <math>\widetilde{\psi}=\psi_{t}-M(\psi) \ </math>
The Lax operators combine to form a multiplicative operator, not a differential operator, of the
: <math>(L_{t}+LM-ML)\psi=0</math>
The Lax operators are chosen to make the multiplicative operator equal to the nonlinear differential equation.{{sfn|Aktosun|2009}}{{rp|4963}}
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