Approximate Symmetries Analysis and Conservation Laws Corresponding to Perturbed Korteweg–de Vries Equation | Zendy

Tahir Ayaz | Zendy; Farhad Ali | Zendy; Wali Khan Mashwani | Zendy; Israr Ali Khan | Zendy; Zabidin Salleh | Zendy; Ikramullah Ikramullah | Zendy

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Approximate Symmetries Analysis and Conservation Laws Corresponding to Perturbed Korteweg–de Vries Equation

Author(s) -

Tahir Ayaz,

Farhad Ali,

Wali Khan Mashwani,

Israr Ali Khan,

Zabidin Salleh,

Ikramullah Ikramullah

Publication year - 2021

Publication title -

journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.252

H-Index - 13

eISSN - 2314-4785

pISSN - 2314-4629

DOI - 10.1155/2021/7710333

Subject(s) - korteweg–de vries equation , mathematics , conservation law , homogeneous space , partial differential equation , perturbation (astronomy) , differential equation , mathematical analysis , nonlinear system , function (biology) , mathematical physics , physics , geometry , quantum mechanics , evolutionary biology , biology

The Korteweg–de Vries (KdV) equation is a weakly nonlinear third-order differential equation which models and governs the evolution of fixed wave structures. This paper presents the analysis of the approximate symmetries along with conservation laws corresponding to the perturbed KdV equation for different classes of the perturbed function. Partial Lagrange method is used to obtain the approximate symmetries and their corresponding conservation laws of the KdV equation. The purpose of this study is to find particular perturbation (function) for which the number of approximate symmetries of perturbed KdV equation is greater than the number of symmetries of KdV equation so that explore something hidden in the system.

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