Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?

share|cite|improve this question
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
share|cite|improve this answer

In terms of the initial value problem, a large class of interesting 1-dimensional questions arise from studying various approximations to surface waves starting from fundamental equations of fluid dynamics.

The Korteweg-de Vries equation and its cousins gKdV and mKdV all lead to demonstrations of a competition between cohesive self-interaction that leads to soliton formation, and dispersive wave-like phenomenon.

(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.)

You can also consider looking at the Benjamin-Bona-Mahony equation, which shows off some long wavelength behaviour (in constrast to the KdV solitons, which tends to be more spatially concentrated).

share|cite|improve this answer
Thank you. Great! – alext87 Jan 29 '11 at 18:04

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.