add BO equation

[MikaelSlevinsky]

• add Hilbert_{\R}{f}(z), the Hilbert transform on the real line for periodic functions on [a,b). This is equivalent to the cotangent version. However, it breaks with the convention of the package that the domain of integration of the singular integral operator should be defined by the domainspace. Perhaps this case could be an exception?
• fix a typo in periodicline

[dlfivefifty]

Probably PeriodicInterval should actually be the line, and evaluation defined for all R by moding. I can't think of an example where you actually want the current behaviour.

We could even rename PeriodicIntercal to "Torus"

(, periodicline is used already to mean a conformally mapped circle.)

Sent from my iPhone

On 20 Dec 2015, at 01:49, Richard Mikael Slevinsky notifications@github.com wrote:

add Hilbert_{\R}{f}(z), the Hilbert transform on the real line for periodic functions on [a,b). This is equivalent to the cotangent version. However, it breaks with the convention of the package that the domain of integration of the singular integral operator should be defined by the domainspace. Perhaps this case could be an exception?

fix a typo in periodicline

You can view, comment on, or merge this pull request online at:

https://github.com/ApproxFun/SingularIntegralEquations.jl/pull/65

Commit Summary

add BO equation File Changes

M .gitignore (2) A examples/Time Evolution PDSIES.ipynb (4052) M src/Operators/Hilbert.jl (69) M src/periodicline.jl (2) Patch Links:

https://github.com/ApproxFun/SingularIntegralEquations.jl/pull/65.patch https://github.com/ApproxFun/SingularIntegralEquations.jl/pull/65.diff — Reply to this email directly or view it on GitHub.

[MikaelSlevinsky]

The Benjamin-Ono equation with periodic boundary conditions (as implemented) has periodic analogues to solitons, so I think that would be interesting to some.

http://www.diva-portal.org/smash/get/diva2:617038/FULLTEXT01.pdf

I guess we just need to figure out what to call the real line with periodicity, i.e. f(t+b-a) = f(t) for all t in R.

I don't think you need to mod for evaluation if the basis is periodic too, it's the perfect extrapolation.