Abstract
To help the understanding of the shallow-water waves, we in this Letter investigate the nearly concentric Korteweg–de Vries equation with computerized symbolic computation, so as to find an auto-Bäcklund transformation and some exact solitonic solutions. We then predict several new non-travelling-wave two-dimensional observable effects that the future fluid experiments might discover. We believe that the combined two-dimensional observations on those features together be more effective or determinant. The “seed” solutions for the auto-Bäcklund transformation have been found, e.g., via the Wu method.
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