A modified Korteweg–de Vries (mKdV)‐type bilinear equation that has been shown to pass the three‐soliton solution and the Painleve´ tests [see, J. Math. Phys.2094, 28 (1987);2572, 31 (1990)] is considered herein. In this article, a Ba¨cklund transformation...
We 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 integrable by the inverse scattering transform. However there are some ...
A family of higher‐order modified Korteweg–de Vries equations with variable coefficients (t‐ho‐mKdV) is introduced. A one‐to‐one correspondence between a real solution of these equations and a complex solution of the variable coefficient higher‐order ...
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 ...
2023, 7(1), 75; https://doi.org/10.3390/fractalfract7010075 ActionDateNotesLink article pdf uploaded. 9 January 2023 16:50 CET Version of Record https://www.mdpi.com/2504-3110/7/1/75/pdf-vor article pdf uploaded. 10 January 2023 02:30 CET Updated version of record https://www.mdpi...