The Dispersion of the Axisymmetric Longitudinal Waves in the Pre-Strained Bi-Material Hollow Cylinder with the Imperfect Interface Conditions

Akbarov, S. D.; Ipek, Cengiz

doi:10.1007/978-94-007-2069-5_93

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2021

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“…Since then, a lot of remarkable work has been done. For hyperelastic materials the main aspects of nonlinear elastodynamics can be found in Chou-Wang et al [4][5][6][7][8][9]. Cohen et al [10] studied the propagation of nonlinear traveling waves in a cylindrical rod composed of a class of compressible Mooney-Rivlin materials and obtained a system of nonlinear evolution equations for describing the symmetrical motion of the rod.…”

Section: Introductionmentioning

confidence: 99%

Nonclassical Lie symmetry and conservation laws of the nonlinear time-fractional Korteweg–de Vries equation

Hashemi

Haji‐Badali

Alizadeh

2021

Commun. Theor. Phys.

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In this paper, we use the symmetry of the Lie group analysis as one of the powerful tools that deals with the wide class of fractional order differential equations in the Riemann–Liouville concept. In this study, first, we employ the classical and nonclassical Lie symmetries (LS) to acquire similarity reductions of the nonlinear fractional far field Korteweg–de Vries (KdV) equation, and second, we find the related exact solutions for the derived generators. Finally, according to the LS generators acquired, we construct conservation laws for related classical and nonclassical vector fields of the fractional far field KdV equation.

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