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...
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 ...
nonlinear wave; cylindrical Korteweg–De Vries equation; soliton; self-similar solitary wave 1. Introduction The study of weakly nonlinear cylindrical waves in dispersive media has a long history. In 1959 Lordansky derived the cylindrical version of the Korteweg–de Vries (cKdV) Equation [1] for...
The reverse space-time nonlocal complex modified Kortewewg–de Vries (mKdV) equation is investigated by using the consistent tanh expansion (CTE) method. According to the CTE method, a nonauto-Bäcklund transformation theorem of nonlocal complex mKdV is obtained. The interactions between one kink...