Joel Klipfel

  • Graduate Student
  • Math Representative to the Graduate Student Congress
  • Chair, Graduate Student Congress Internal Affairs Committee
  • Mathematics
802 Patterson Office Tower
Other Affiliations:
  • Math Department Representative for the Graduate Student Congress
  • Chair of the Internal Affairs Committee for the Graduate Student Congress
Research Interests:
PhD Dissertation Project Summary:

In the early 1980’s, Kodama, Ablowitz and Satsuma, together with Santini, Ablowitz and Fokas, developed the formal inverse scattering theory of the Intermediate Long Wave (ILW) equation and explored its connections with the Benjamin-Ono (BO) and KdV equations. The ILW equation

 

models the behavior of long internal gravitational waves in stratified fluids of depth 0<δ<, where T is a singular operator which dependes on the depth δ. In the limit δ0, the ILW reduces to the Korteweg de Vries (KdV) equation, and in the limit δ, the ILW (at least formally) reduces to the Benjamin-Ono (BO) equation.

While the KdV equation is very well understood, a rigorous analysis of inverse scattering for the ILW equation remains to be accomplished. There is currently no rigorous proof that the inverse scattering procedure outlined by Kodama et al. solves the ILW, even for small data. My advisor, Peter Perry, our collaborator from the University of Oklahoma, Yilun "Allen" Wu, and I are working to ameliortate this situation.

 

MA 214 Office Hours:

Monday: 11am to 12pm in 802 POT

Wednesday: 2pm to 3pm in the Klein Room in Mathskeller (CB 63)

Friday: 11am to 12pm in 802 POT

Selected Publications: 
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