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- W2127247738 abstract "The (scalar) sine-Gordon equation appears in many interesting contexts, such as the description of surfaces of constant negative Gaussian curvature (Bour, 1862; Eisenhart, 1960), magnetic flux propagation in Josephson junctions (McLaughlin & Scott, 1978; Mineev & Shmidt, 1980) and propagation of deformations along the DNA double helix (Gaeta et al., 1994; Lennholm & Hornquist, 2003; Salerno, 1991; Yakushevich, 2004). Because of the importance of the applications in which the sine-Gordon equation arises (see Aktosun et al., 2010 for details), it is not surprising that different approaches, such as the IST (Ablowitz et al., 1973), and Darboux and Backlund transformations (Gu et al., 2005; Rogers & Schief, 2002), were developed to get exact solutions. These exact solutions are written in terms of elementary functions and, in Lamb (1980) and Poppe (1983), the reader can find many of the solutions coming from the methods cited above. In Aktosun et al. (2010), we have presented a family of explicit solutions to the sine-Gordon equation uxt = sin(u) (1)" @default.
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- W2127247738 date "2012-05-28" @default.
- W2127247738 modified "2023-09-25" @default.
- W2127247738 title "Closed form solutions to the matrix sine-Gordon equation" @default.
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- W2127247738 doi "https://doi.org/10.1093/imamat/hxs029" @default.
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