Lie symmetry analysis, power series solutions and conservation laws of the time-fractional breaking soliton equation. Issue 6 (2nd November 2022)

• Record Type: Journal Article
• Authors: Zhang, Zhi-Yong; Zhu, Hui-Min; Zheng, Jia
• Is Part Of: Waves in random and complex media. Volume 32:Issue 6(2022)
• Page Start: 3032
• Page End: 3052
• Publication Date: 2022-11-02
• Subjects: Lie symmetry -- prolongation formula -- conservation law -- power series solution -- time-fractional breaking soliton equation; Electromagnetic waves -- Periodicals; Electromagnetic waves -- Scattering -- Periodicals; 531.1133
• DOI: 10.1080/17455030.2022.2042427
• Languages: English
• ISSNs: 1745-5030

Abstract

Abstract : The main attention of this work focus on extending the Lie symmetry and conservation law theories to the fractional partial differential equations involving the mixed derivative of the Riemann-Liouville time-fractional and first-order x -derivatives. More specifically, we first present a new prolongation formula of the infinitesimal generators of Lie symmetries for the time-fractional breaking soliton equation since the equation involves the mixed derivative, then perform Lie symmetry analysis for the equation. Furthermore, we construct an optimal system of one-dimensional Lie subalgebras and use them to reduce the equation to lower-dimensional fractional partial differential equations involving the Erdélyi-Kober operator. In order to construct the power series solution of the equation, we introduce the Hadamard's finite-part integral to deal with the divergence of the integrals. The convergence and error estimate of the power series solution are proved. Finally, a new conservation law formula for the equation is given by means of the nonlinear self-adjointness method and nontrivial conservation laws are found.