 Integral complex modified Korteweg-de Vries (Icm-KdV) equationsM. Velasco-Juan and J. Fujioka Chaos, Solitons & Fractals, 2020, vol. 134, issue C Abstract: In this article we examine different ways of introducing nonlocal effects in the complex modified Korteweg-de Vries (cmKdV) equation. Four possible nonlocal generalizations of the cmKdV equation are presented. In these variants of the cmKdV equation the nonlinear term has been replaced by one, two, or three integral terms. Three of these variants can be obtained by the least action principle, and they possess different equivalent Lagrangians. The relationship between these Lagrangians is entirely new. Therefore, a novel type of Lagrangian equivalence has been found. As Fubini´s theorem is needed to prove the equivalence of these Lagrangians, we call them “F-equivalent”. Noether´s theorem is applied to these integral equations, and different conserved quantities are obtained. The behavior of solitary waves in these models is also studied. It was found that one of these models has soliton-like solutions. Numerical solutions show that these solitons are stable, and the amplitudes of perturbed solitons attain constant values after a short transient period. Finally, a variational method was applied to get a better understanding of the behavior of these pulses during the transient periods. Date: 2020 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:134:y:2020:i:c:s0960077920300898 DOI: 10.1016/j.chaos.2020.109687 Access Statistics for this article Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros More articles in Chaos, Solitons & Fractals from Elsevier |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.