Linear and nonlinear generalized Fourier transforms
Pelloni, B. (2006) Linear and nonlinear generalized Fourier transforms. Philosophical Transactions of the Royal Society a-Mathematical Physical and Engineering Sciences, 364 (1849). pp. 3231-3249. ISSN 1364-503X
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This article presents an overview of a transform method for solving linear and integrable nonlinear partial differential equations. This new transform method, proposed by Fokas, yields a generalization and unification of various fundamental mathematical techniques and, in particular, it yields an extension of the Fourier transform method.