<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>Many curve evolutions have been determined which are integrable in recent times. The motion of curves can be defined by certain integrable equations including the modified Korteweg-de Vries. In this study, the quaternionic curves in 3 and 4-dimensional Euclidean spaces have been considered and the motions of inextensible quaternionic curves have been characterized by the modified Korteweg-de Vries (mKdV) equations. For this purpose, the basic concepts of the quaternions and quaternionic curves have been summarized. Then the evolutions of inextensible quaternionic curves with reference to the Frenet formulae have been obtained. Finally, the mKdV equations have been generated with the help of their evolutions</p>
</abstract>

Many curve evolutions have been determined which are integrable in recent times. The motion of curves can be defined by certain integrable equations including the modified Korteweg-de Vries. In this study, the quaternionic curves in 3 and 4-dimensional Euclidean spaces have been considered and the motions of inextensible quaternionic curves have been characterized by the modified Korteweg-de Vries (mKdV) equations. For this purpose, the basic concepts of the quaternions and quaternionic curves have been summarized. Then the evolutions of inextensible quaternionic curves with reference to the Frenet formulae have been obtained. Finally, the mKdV equations have been generated with the help of their evolutions

Motion of Inextensible Quaternionic Curves and Modified Korteweg-de Vries Equation

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Many curve evolutions have been determined which are integrable in recent times. The motion of curves can be defined by certain integrable equations including...

Motion of Inextensible Quaternionic Curves and Modified Korteweg-de Vries Equation

Published Online: Jun 02, 2022

Page range: 91 - 101

Received: Aug 10, 2021

Accepted: Nov 10, 2021

DOI: https://doi.org/10.2478/auom-2022-0020

Keywords
Modified Korteweg-de Vries equation, quaternionic curve, evolution curve, inextensible curve

© 2022 Kemal Eren, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Motion of Inextensible Quaternionic Curves and Modified Korteweg-de Vries Equation

Published Online: Jun 02, 2022

Page range: 91 - 101

Received: Aug 10, 2021

Accepted: Nov 10, 2021

DOI: https://doi.org/10.2478/auom-2022-0020

KeywordsModified Korteweg-de Vries equation, quaternionic curve, evolution curve, inextensible curve

© 2022 Kemal Eren, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Modified Korteweg-de Vries equation, quaternionic curve, evolution curve, inextensible curve