Quaternion-Valued Rational Solutions to the KdV Equation
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Serna, Albert
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Abstract
In this Master's Thesis we look at the KdV equation in a non-commutative setting. While the study of the KdV equation in non-commutative settings is not in and of itself new, we focus specifically on the quaternions. We construct the quaternion-valued rational solutions of the KdV Equation given any element of Φ of an infinite dimensional vector space V. The main result of this paper shows that any solution produced from an element of V could be produced using an element chosen from the proper subspace V' of V.