# One dimensional boundary value problems showing interesting behaviour

I want to show some users of a piece of software some solutions of one-dimension boundary value problems (can also be initial value problems). I'm after a collection of problems whose solutions are very interesting or the BVP are of a particularly interesting nature. The problems can be linear or non-linear. Does anyone have any suggests?

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Wiki-ized: this is a question looking for examples. –  Willie Wong Jan 28 '11 at 18:31
What do you mean by 1D BVP? Is it only ODEs or PDEs in 1D space + time that you are talking about? In the latter case, it is clearer to call them initial-boundary value problems. –  timur Jan 29 '11 at 12:48

This(site about boundary value problems) should be useful. Some of the interesting boundary value problems they list are the following:

• Heat Equation
• Wave Equation
• Laplace Equation
• Poisson Equation
• Schrodigner's Equation
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(What is especially interesting is to look at the purely dispersive part of the KdV equation $$\partial_t \phi + \partial_x^3 \phi = 0$$ and the purely transport part of the equation $$\partial_t \phi + \phi\partial_x\phi = 0$$ and note their characteristic behaviours. Then compare it against various different initial data for the KdV equation.)