Co-Author(s): John Cobb, Alex Kasman, Monique Sparkman, and Albert Serna
Abstract:
Although both the KdV Equation and quaternions are already well-studied, this talk will demonstrate that this student research project generated some interesting and new results about their intersection. We utilize the unique properties of quaternions to develop new methods for producing and understanding the behavior of these non-commutative KdV solutions. The main theorem characterizing the non-linear super-position of breather solitons with other solutions gives what I believe are new results even in the real/commutative case.