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 ...
The Korteweg–de Vries (KDV) equation is one of the most well-known models in nonlinear physics, such as fluid physics, plasma, and ocean engineering. It is very important to obtain the exact solutions of this model in the process of studying these topics. In the present paper, using dist...
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...
We consider approximate, exact, and numerical solutions to the cylindrical Korteweg–de Vries equation. We show that there are different types of solitary waves and obtain the dependence of their parameters on distance. Then, we study the interaction of
Sasa–Satsuma (SS)-type integrable matrix modified Korteweg–de Vries (mKdV) equations are derived from two group constraints, involving the replacement of the spectral matrix in the Ablowitz–Kaup–Newell–Segur matrix eigenproblems with its matrix transpose and its Hermitian transpose. Using the Lax...
On the Dynamical Behavior of Solitary Waves for Coupled Stochastic Korteweg–De Vries Equations. Mathematics. 2023; 11(16):3506. https://doi.org/10.3390/math11163506 Chicago/Turabian Style Mohammed, Wael W., Farah M. Al-Askar, and Clemente Cesarano. 2023. "On the Dynamical Behavior of ...
This article introduces two kinds of processing techniques to solve Jacobian elliptic equations and obtain rich periodic wave solutions. Then, the equation was used as an auxiliary equation to solve the (3+1)-dimensional modified Korteweg de Vries–Zakha