On the global uniqueness of Stokes' wave of extreme form

K. Kobayashi
2010 IMA Journal of Applied Mathematics  
We present a computer-assisted proof of global uniqueness of Stokes' wave of extreme form. Stokes' wave of extreme form is a water wave which forms a corner of 120 degrees at the crest, and is considered to be the limit of the positive solution of Nekrasov's equation which expresses periodic gravity waves of permanent form on the free surface. The numerical verification method plays an important role in the proof. As for the global uniqueness of Stokes' wave of extreme form, it is not only a
more » ... it is not only a longtime open problem, but also it is related to an important conjecture which is called Stokes' conjecture.
doi:10.1093/imamat/hxq037 fatcat:hhadpxmxtff35p5kvmccif67y4