**Korteweg–de Vries Equation**

This article describe about Korteweg–de Vries Equation (KdV), which means of elementary operations as well as by using Bäcklund transform. Special interest is devoted to non-linear superposition of several waves, the so called Solitary Waves or Solitons which is performed by Bäcklund transform too. It is particularly notable as the prototypical example of an exactly solvable model, that is, a non-linear partial differential equation whose solutions can be exactly and precisely specified. The mathematical theory behind the KdV equation is a topic of active research.

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