Is This Equation Known as the Korteweg-de Vries Equation? • Physics Forums

Dustinsfl · 2013-09-03T23:45:06+00:00

\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?

Thread 'Direction Fields and Isoclines'

I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...

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

Thread 'Direction Fields and Isoclines'

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