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Research Interests
 
Nonlinear Dispersive Partial Differential Equations, Applied Mathematics ; especially I am interested on nonlinear Schrodinger and KdV equations, standing waves, solitons, multi-solitons, orbital stability and instability, and variational methods.
 
Publications
 
  • J. Albert and S. Bhattarai, Concentration compactness and the stability of solitary-wave solutions for a Schrodinger-KdV system. (In preparation)

 

  • J. Albert and S. Bhattarai, Existence and stability of solitary-wave solutions for an equation of short and long dispersive waves. (In preparation)

 

If you are interested in learning about nonlinear dispersive equations, here are some good online resources.

  • DispersiveWiki Project (For comprehensive information about the latest results, conjectures, bibliography, concepts, and other materials for nonlinear dispersive and wave equations).
  • Soliton Page maintained by R. Victor Jones
  • Alex Kasman Soliton Page

 

It is important to have a solid foundation in analysis, particularly functional analysis and Sobolev spaces. Here are some books on basis tools of anaysis and nonlinear dispersive equations.

  • Sobolev Spaces, R.A. Adams, Academic Press, New York, 1975.
  • Nonlinear Dispersive Equations : Local and Global Analysis, Terence Tao, CBMS Regional Conference Series in Mathematics.
  • Introduction to Nonlinear Dispersive Equations, F. Linares and G. Ponce, Springer.

 

It is important to have a solid foundation in analysis, particularly functional analysis and Sobolev spaces. Here are some books on basis tools of anaysis.