A model of solitary waves in a nonlinear elastic circular rod: Abundant different type exact solutions and conservation laws


Çelik N., Seadawy A. R. , Sağlam Özkan Y., Yaşar E.

Chaos, Solitons and Fractals, vol.143, 2021 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 143
  • Publication Date: 2021
  • Doi Number: 10.1016/j.chaos.2020.110486
  • Journal Name: Chaos, Solitons and Fractals
  • Journal Indexes: Science Citation Index Expanded, Scopus, Academic Search Premier, INSPEC, zbMATH
  • Keywords: Nonlinear elastic circular rod, Exact solutions, Conservation laws

Abstract

© 2020 Elsevier LtdIn this study, we have dealt with a wave equation containing 4th order nonlinear mixed derivative. This model corresponds to solitary waves in nonlinear elastic circular rod. One dimensional optimal systems corresponding to Lie symmetry generator sub-algebras, symmetry reductions, and group invariant solutions corresponding to these systems have been systematically produced by Lie symmetry analysis of this model. In addition, traveling wave solutions were obtained with the help of an useful integration scheme of the model. These solutions are structures with physical properties of hyperbolic, trigonometric and rational solution types. Numerical simulations of the obtained solutions for different values of the parameters were made. The stability property of the obtained solutions is tested to show the ability of obtained solutions. In addition, the local conservation laws of the model were obtained with the help of the multiplier homotopy method.