Dynamical Soliton Wave Structures of One-Dimensional Lie Subalgebras via Group-Invariant Solutions of a Higher-Dimensional Soliton Equation with Various Applications in Ocean Physics and Mechatronics Engineering  

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作  者:Oke Davies Adeyemo Chaudry Masood Khalique 

机构地区:[1]International Institute for Symmetry Analysis and Mathematical Modelling,Department of Mathematical Sciences,North-West University,Mafikeng Campus,Private Bag X 2046,Mmabatho 2735,Republic of South Africa

出  处:《Communications on Applied Mathematics and Computation》2022年第4期1531-1582,共52页应用数学与计算数学学报(英文)

基  金:the North-West University,Mafikeng campus for its continued support.

摘  要:Having realized various significant roles that higher-dimensional nonlinear partial differ-ential equations(NLPDEs)play in engineering,we analytically investigate in this paper,a higher-dimensional soliton equation,with applications particularly in ocean physics and mechatronics(electrical electronics and mechanical)engineering.Infinitesimal generators of Lie point symmetries of the equation are computed using Lie group analysis of differen-tial equations.In addition,we construct commutation as well as Lie adjoint representation tables for the nine-dimensional Lie algebra achieved.Further,a one-dimensional optimal system of Lie subalgebras is also presented for the soliton equation.This consequently enables us to generate abundant group-invariant solutions through the reduction of the understudy equation into various ordinary differential equations(ODEs).On solving the achieved nonlinear differential equations,we secure various solitonic solutions.In conse-quence,these solutions containing diverse mathematical functions furnish copious shapes of dynamical wave structures,ranging from periodic,kink and kink-shaped nanopteron,soliton(bright and dark)to breather waves with extensive wave collisions depicted.We physically interpreted the resulting soliton solutions by imploring graphical depictions in three dimensions,two dimensions and density plots.Moreover,the gained group-invariant solutions involved several arbitrary functions,thus exhibiting rich physical structures.We also implore the power series technique to solve part of the complicated differential equa-tions and give valid comments on their results.Later,we outline some applications of our results in ocean physics and mechatronics engineering.

关 键 词:Higher-dimensional soliton equation Lie group analysis One-dimensional optimal system of Lie subalgebras Exact soliton solutions Conserved currents 

分 类 号:O17[理学—数学]

 

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