Is This Equation Known as the Korteweg-de Vries Equation?

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SUMMARY

The equation presented, defined as ψ_t + ψ_{xxx} + f(ψ)ψ_x = 0, is identified as the Korteweg-de Vries (KdV) equation. This equation is significant in the study of nonlinear wave phenomena and is known to lead to the nonlinear Schrödinger equation. The KdV equation is crucial in various fields, including fluid dynamics and mathematical physics, due to its applications in describing shallow water waves.

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Dustinsfl
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\begin{align*}
\psi_t + \psi_{xxx} + f(\psi)\psi_x &= 0
\end{align*}

This equation leads to the nonlinear Shrodinger equation but does this equation have a name?
 
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