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Construction of conservation laws for the Gardner equation,landau-ginzburg-higgs equation,and Hirota-Satsuma equation

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Communications in Theoretical Physics 2024年第5期76卷 49-57页

作者： Cheng Chen Faiza Afzal Yufeng Zhang School of Mathematics China University of Mining and TechnologyXuzhou221116China Jiangsu Center for Applied Mathematics(CUMT) XuzhouJiangsu 221116China

In this paper,two different methods for calculating the conservation laws are used,these are the direct construction of conservation laws and the conservation theorem proposed by *** these two methods,we obtain the co... 详细信息

关键词： conservation laws landau-ginzburg-higgs equation Hirota-Satsuma equation Gardner equation

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Conserved vectors and symmetry solutions of the landau–ginzburg–higgs equation of theoretical physics

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Communications in Theoretical Physics 2024年第4期76卷 51-65页

作者： Chaudry Masood Khalique Mduduzi Yolane Thabo Lephoko Material Science Innovation and Modelling Research Focus AreaDepartment of Mathematical SciencesNorth-West UniversityMafikeng CampusPrivate Bag X 2046Mmabatho 2735South Africa

This paper is devoted to the investigation of the landau–ginzburg–higgs equation(LGHe),which serves as a mathematical model to understand phenomena such as superconductivity and cyclotron *** LGHe finds applications in various scientific fields,including fluid dynamics,plasma physics,biological systems,and *** study adopts Lie symmetry analysis as the primary framework for *** analysis involves the identification of Lie point symmetries that are admitted by the differential *** leveraging these Lie point symmetries,symmetry reductions are performed,leading to the discovery of group invariant *** obtain explicit solutions,several mathematical methods are applied,including Kudryashov's method,the extended Jacobi elliptic function expansion method,the power series method,and the simplest equation *** methods yield solutions characterized by exponential,hyperbolic,and elliptic *** obtained solutions are visually represented through 3D,2D,and density plots,which effectively illustrate the nature of the *** plots depict various patterns,such as kink-shaped,singular kink-shaped,bell-shaped,and periodic ***,the paper employs the multiplier method and the conservation theorem introduced by Ibragimov to derive conserved *** conserved vectors play a crucial role in the study of physical quantities,such as the conservation of energy and momentum,and contribute to the understanding of the underlying physics of the system.

关键词： landau-ginzburg-higgs equation Lie symmetry analysis group invariant solutions conserved vectors multiplier method Ibragimov's method

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Multi-symplectic Runge-Kutta methods for landau-ginzburg-higgs equation

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Applied Mathematics and Mechanics(English Edition) 2009年第8期30卷 1027-1034页

作者：胡伟鹏邓子辰韩松梅范玮 School of Mechanics Civil Engineering and Architecture Northwestern Polytechnical University School of Power and Energy Northwestern Polytechnical University State Key Laboratory of Structural Analysis of Industrial Equipment Dalian Universityof Technology

Nonlinear wave equations have been extensively investigated in the last sev- eral decades. The landau-ginzburg-higgs equation, a typical nonlinear wave equation, is studied in this paper based on the multi-symplectic theory in the Hamilton space. The multi-symplectic Runge-Kutta method is reviewed, and a semi-implicit scheme with certain discrete conservation laws is constructed to solve the first-order partial differential equations （PDEs） derived from the landau-ginzburg-higgs equation. The numerical re- sults for the soliton solution of the landau-ginzburg-higgs equation are reported, showing that the multi-symplectic Runge-Kutta method is an efficient algorithm with excellent long-time numerical behaviors.

关键词： multi-symplectic landau-ginzburg-higgs equation Runge-Kutta method conservation law soliton solution

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