Geodesic
New solutions of the Schwarzian Korteweg–de Vries equation in $2{+}1$ dimensions based on weak symmetries
Teoretičeskaâ i matematičeskaâ fizika, Tome 151 (2007) no. 3, pp. 380-390 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the $(2+1)$-dimensional integrable Schwarzian Korteweg–de Vries equation. Using weak symmetries, we obtain a system of partial differential equations in $1+1$ dimensions. Further reductions lead to second-order ordinary differential equations that provide new solutions expressible in terms of known functions. These solutions depend on two arbitrary functions and one arbitrary solution of the Riemann wave equation and cannot be obtained by classical or nonclassical symmetries. Some of the obtained solutions of the Schwarzian Korteweg–de Vries equation exhibit a wide variety of qualitative behaviors; traveling waves and soliton solutions are among the most interesting.
Keywords: weak symmetry, partial differential equation, solitary wave. 
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     title = {New solutions of {the~Schwarzian} {Korteweg{\textendash}de} {Vries} equation in $2{+}1$ dimensions based on weak symmetries},
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M. L. Gandarias; M. S. Bruzón. New solutions of the Schwarzian Korteweg–de Vries equation in $2{+}1$ dimensions based on weak symmetries. Teoretičeskaâ i matematičeskaâ fizika, Tome 151 (2007) no. 3, pp. 380-390. http://geodesic.mathdoc.fr/item/TMF_2007_151_3_a5/

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