Can the Inverse Scattering Transform Solve PDEs?

saravanan13
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Can anyone help me to solve the PDE via Inverse Scattering transform method?
 
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saravanan13 said:
Can anyone help me to solve the PDE via Inverse Scattering transform method?

You can't "solve PDE" via IST. You can solve only the Cauchy problem associated with that PDE using the Inverse Scattering Transform. It's not an easy task to do.
First try checking at these links:
http://en.wikipedia.org/wiki/Inverse_scattering_transform"
http://www.primat.mephi.ru/wiki/ow.asp?Korteweg-de_Vries_equation%2FInverse_scattering_transform"
 
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Thread 'Direction Fields and Isoclines'

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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