Brian Pigott

Uniqueness for sums of nonvanishing squares Published in Integers, 2020We address the issue of uniqueness for sums of nonvanishing squares; that is, we determine all positive integers N that can be represented as a sum of k 5 nonvanishing squares in essentially only one way. Our methods are elementary and are based on a lower bound on the number of 1s that must be present in such a representation.Recommended citation: N. Kosovalic and B. Pigott, "Uniqueness for sums of nonvanishing squares." Integers. 20 (2020). http://math.colgate.edu/~integers/u93/u93.pdf _(PDF)

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Nonlinear profile decomposition and the concentration phenomenon for supercritical generalized KdV equations Published in Indiana University Mathematics Journal, 2018A nonlinear profile decomposition is established for solutions of supercritical generalized Korteweg-de Vries equations. As a consequence, we obtain a concentration result for finite-time blow-up solutions that are of type II.Recommended citation: L.G. Farah and B. Pigott, "Nonlinear profile decomposition and the concentration phenomenon for supercritical generalized KdV equations." Indiana Univ. Math. J.. 67 (5) (2018). https://doi.org/10.1512/iumj.2018.67.7471

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