Lie symmetry analysis of a stochastic gene evolution in double-chain deoxyribonucleic acid system. Issue 6 (2nd November 2022)

• Record Type: Journal Article
• Authors: Saleh, R.; Mabrouk, S. M.; Wazwaz, Abdul-Majid
• Is Part Of: Waves in random and complex media. Volume 32:Issue 6(2022)
• Page Start: 2903
• Page End: 2917
• Publication Date: 2022-11-02
• Subjects: Lie infinitesimals -- singular Manifolds method -- Schwarzian derivative -- double-chain deoxyribonucleic acid; Electromagnetic waves -- Periodicals; Electromagnetic waves -- Scattering -- Periodicals; 531.1133
• DOI: 10.1080/17455030.2020.1871109
• Languages: English
• ISSNs: 1745-5030

Abstract

ABSTRACT: In this work, we study the double chain Deoxyribonucleic acid (DNA) model, the study will be carried out by using two analytical methods, namely, Lie transformation method, then combined with the singular manifold method (SMM). Six cases are studied for different vector combinations. Two successive symmetry reductions transform the equation to an ordinary differential equation (ODE). We next apply the singular manifold method to the obtained ordinary differential equations. This will result in a Schwarzian derivative whose solution leads to soliton solutions for longitudinal and transversal motions. The solutions contain different types of wave solutions, N-solitons, kink and periodic wave solutions. Some of the resulting solutions are graphically illustrated.