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Periodic waves of the non dissipative double dispersive micro strain wave in the micro structured solids

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  • Gao, Wei
  • Silambarasan, Rathinavel
  • Baskonus, Haci Mehmet
  • Anand, R. Vijay
  • Rezazadeh, Hadi

Abstract

The non dissipative double dispersive micro strain wave in the micro structured solid is solved via the F-expansion method and obtained the new exact doubly periodic Jacobi elliptic function solutions. The F-expansion method converts the nonlinear partial differential equation into ordinary differential equation, then the initially assumed solution converts the ordinary differential equation into systems of algebraic equations. By solving these algebraic equations, the six families of the periodic wave solutions are classified of which three are real valued and three are complex valued. Next by treating the Jacobi elliptic function modulus to 0 (or) 1, some of the new exact solitons and their classifications are obtained. The two dimensional and three dimensional graphs are plotted to show the traversing of the obtained wave trains.

Suggested Citation

  • Gao, Wei & Silambarasan, Rathinavel & Baskonus, Haci Mehmet & Anand, R. Vijay & Rezazadeh, Hadi, 2020. "Periodic waves of the non dissipative double dispersive micro strain wave in the micro structured solids," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    • Handle: RePEc:eee:phsmap:v:545:y:2020:i:c:s0378437119321004
    DOI: 10.1016/j.physa.2019.123772
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    References listed on IDEAS

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    1. Cattani, Carlo & Ciancio, Armando, 2016. "On the fractal distribution of primes and prime-indexed primes by the binary image analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 460(C), pages 222-229.
    2. Prakash, Amit & Kumar, Manoj & Sharma, Kapil K., 2015. "Numerical method for solving fractional coupled Burgers equations," Applied Mathematics and Computation, Elsevier, vol. 260(C), pages 314-320.
    3. Prakash, Amit & Kumar, Manoj & Baleanu, Dumitru, 2018. "A new iterative technique for a fractional model of nonlinear Zakharov–Kuznetsov equations via Sumudu transform," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 30-40.
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    Cited by:

    1. Silambarasan, Rathinavel & Nisar, Kottakkaran Sooppy, 2023. "Doubly periodic solutions and non-topological solitons of 2+1− dimension Wazwaz Kaur Boussinesq equation employing Jacobi elliptic function method," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    2. Silambarasan, Rathinavel & Kılıçman, Adem, 2023. "Solitons of dispersive wave steered from Navier–Bernoulli and Love’s hypothesis in cylindrical elastic rod with compressible Murnaghan’s materials," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 699-720.
    3. Silambarasan, Rathinavel & Baskonus, Haci Mehmet & Vijay Anand, R. & Dinakaran, M. & Balusamy, Balamurugan & Gao, Wei, 2021. "Longitudinal strain waves propagating in an infinitely long cylindrical rod composed of generally incompressible materials and its Jacobi elliptic function solutions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 566-602.

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