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 . ...
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...
A family of traveling solitary wave solutions including soliton, kink, periodic and singular solutions of the nonlocal mKdV equation is discussed [16]. The interaction between solitons and a periodic cnoidal wave of the Korteweg–de Vries equation and the cubic Schrödinger equation is discussed ...
Model construction for different physical situations, and developing their solutions, are the major characteristics of the scientific work in physics and engineering. Korteweg–de Vries (KdV) models are very important due to their ability to capture diff