Various soliton solutions and asymptotic state analysis for the discrete modified Korteweg-de Vries equation
type: Item
instance of: scholarly article
title: Various soliton solutions and asymptotic state analysis for the discrete modified Korteweg-de Vries equation
zbMATH Open document ID: 1479.35741
DOI: 10.1155/2021/3445894
author: Zhe Lin
author: Xiao-Yong Wen
author: Meng-Li Qin
published in: Advances in Mathematical Physics
publication date: 2021-11-25T00:00:00Z
review text: Summary: Under investigation is the discrete modified Korteweg-de Vries (mKdV) equation, which is an integrable discretization of the continuous mKdV equation that can describe some physical phenomena such as dynamics of anharmonic lattices, solitary waves in dusty plasmas, and fluctuations in nonlinear optics. Through constructing the discrete generalized \((m, N - m)\)-fold Darboux transformation for this discrete system, the various discrete soliton solutions such as the usual soliton, rational soliton, and their mixed soliton solutions are derived. The elastic interaction phenomena and physical characteristics are discussed and illustrated graphically. The limit states of diverse soliton solutions are analyzed via the asymptotic analysis technique. Numerical simulations are used to display the dynamical behaviors of some soliton solutions. The results given in this paper might be helpful for better understanding the physical phenomena in plasma and nonlinear optics.
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 35Q51
Mathematics Subject Classification ID: 35C08
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 37K35
Mathematics Subject Classification ID: 82D10
Mathematics Subject Classification ID: 78A60
zbMATH DE Number: 7433482
zbMATH Keywords: Korteweg-de Vries equation
zbMATH Keywords: solitary waves in dusty plasmas
zbMATH Keywords: fluctuations in nonlinear optics
describes a project that uses: Matlab
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/3445894
OpenAlex ID: W3203251786
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description: scientific article; zbMATH DE number 7433482