An integrable partial differential equation has enough exact structure, such as a Lax pair, infinitely many conserved quantities, or an inverse scattering transform, to reduce its evolution to auxiliary linear or finite-dimensional data.
The Harry Dym equation is the integrable partial differential equation . It admits a Lax pair based on the second-order operator .
The Boussinesq equation is a nonlinear dispersive wave equation. One integrable normalization is
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