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

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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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Thread 'A question about variables of integration'

I have the equation ##F^x=m\frac {d}{dt}(\gamma v^x)##, where ##\gamma## is the Lorentz factor, and ##x## is a superscript, not an exponent. In my textbook the solution is given as ##\frac {F^x}{m}t=\frac {v^x}{\sqrt {1-v^{x^2}/c^2}}##. What bothers me is, when I separate the variables I get ##\frac {F^x}{m}dt=d(\gamma v^x)##. Can I simply consider ##d(\gamma v^x)## the variable of integration without any further considerations? Can I simply make the substitution ##\gamma v^x = u## and then...
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