Completely integrable

A few nonlinear dispersive and wave equations are lucky enough to be completely integrable. This means in particular that they enjoy infinitely many conservation laws, and can often be solved by inverse scattering techniques.

List of completely integrable nonlinear dispersive and wave equations

• Benjamin-Ono equation
• One dimensional cubic NLS
• Davey-Stewartson system
• Kadomtsev-Petviashvili equation
• Korteweg-de Vries equation, and more generally the KdV hierarchy
• Modified Korteweg-de Vries equation
• Sine-Gordon equation
• One-dimensional wave maps