A note on “Jacobi elliptic function solutions for the modified Korteweg–de Vries equation”

Liu, Hong-Zhun

doi:10.1016/j.jksus.2014.01.002

Cited by 2 publications

(1 citation statement)

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“…Gardner et al [15] proved both the existence and uniqueness of solutions to the KdV equation. Liu [16] provided an elliptic Jacobi function solution for the KdV equation. In the same research paper, Hufford and Xing [17] reported a numerical solution for the linearized version of the problem as well as superconvergence for the approach used.…”

Section: Introductionmentioning

confidence: 99%

Differential Quadrature Method to Examine the Dynamical Behavior of Soliton Solutions to the Korteweg-de Vries Equation

Mishra

Arora

Emadifar

et al. 2022

Advances in Mathematical Physics

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Nonlinear evolution equations are crucial for understanding the phenomena in science and technology. One such equation with periodic solutions that has applications in various fields of physics is the Korteweg-de Vries (KdV) equation. In the present work, we are concerned with the implementation of a newly defined quintic B-spline basis function in the differential quadrature method for solving the Korteweg-de Vries (KdV) equation. The results are presented using four experiments involving a single soliton and the interaction of solitons. The accuracy and efficiency of the method are presented by computing the L 2 and L ∞ norms along with the conservational quantities in the forms of tables. The results show that the proposed scheme not only gives acceptable results but also consumes less time, as shown by the CPU for the elapsed time in two examples. The graphical representations of the obtained numerical solutions are compared with the exact solution to discuss the nature of solitons and their interactions for more than one soliton.

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Section: Introductionmentioning

confidence: 99%