 ##  [Korteweg–De Vries Equation](/korteweg-de-vries-equation) 

  ##  [Korteweg–De Vries Equation](https://mathlogic.quantumdictionary.io/korteweg-de-vries-equation-0) 

  
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**Mathematics &amp; Logic Dictionary**

 
Definition

A nonlinear dispersive partial differential equation (canonical form u_t + 6 u u_x + u_{xxx} = 0) modeling unidirectional long, shallow-water waves and solitary waves produced by a balance between nonlinear steepening and linear dispersion.