Inverse scattering transform, KdV, and solitons

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Inverse scattering transform, KdV, and solitons

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Aktosun, Tuncay

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2003-05

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In this review paper, the Korteweg-de Vries equation (KdV) is considered, and it is derived by using the Lax method and the AKNS method. An outline of the inverse scattering problem and of its solution is presented for the associated Schrödinger equation on the line. The inverse scattering transform is described to solve the initial-value problem for the KdV, and the time evolution of the corresponding scattering data is obtained. Soliton solutions to the KdV are derived in several ways.

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Institute for Mathematics and Its Applications>IMA Preprints Series

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Aktosun, Tuncay. (2003). Inverse scattering transform, KdV, and solitons. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/3929.

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