de Vries equationPainlevépropertyExact solutionPainlevétestLogistic functionWe consider the Korteweg–de Vries equation with a source. The source depends on the solution as polynomials with constant coefficients. Using the Painlevé test we show that the generalized Korteweg–de Vries equation is not ...
A study of solutions of the Gel'fand–Levitan equation permits one to establish new Bäcklund transformations for the Korteweg–de Vries equation. To a specific change in the scattering parameters, there corresponds a family of Bäcklund transformations. A means to construct these transformations ...
Therefore, the integrability of this mKdV‐type bilinear equation is confirmed.Xing&hyphenBiao Hujournal of mathematical physicsA B\"acklund transformation and nonlinear superposition formula of a modified Korteweg-de Vries-type bilinear equation. Xing-Biao Hu. Journal of Mathematical Physics . ...
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