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Rarely does a nonlinear differential equation, especially a nonlinear partial differential equation, have a closed-form solution. But that is the case for the Korteweg–De Vries equation. (Technically I should say it’s rare for a naturally-occurring nonlinear differential equation to have a closed-form solution. You can always start with a solution and cook up a contrived […] The post Solitons and the KdV equation first appeared on John D. Cook....