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Traveling wave solutions for the hyperbolic Cahn–Allen equation

Author

Listed:
  • Nizovtseva, I.G.
  • Galenko, P.K.
  • Alexandrov, D.V.

Abstract

Traveling wave solutions of the hyperbolic Cahn–Allen equation are obtained using the first integral method, which follows from well-known Hilbert–Nullstellensatz theorem. The obtained complete class of traveling waves consists of continual and singular solutions. Continual solutions are represented by tanh -profiles and singular solutions exhibit unbounded discontinuity at the origin of coordinate system. With the neglecting inertia of the dynamical system, the obtained traveling waves include the previous solutions for the parabolic Cahn–Allen equation.

Suggested Citation

  • Nizovtseva, I.G. & Galenko, P.K. & Alexandrov, D.V., 2017. "Traveling wave solutions for the hyperbolic Cahn–Allen equation," Chaos, Solitons & Fractals, Elsevier, vol. 94(C), pages 75-79.
    • Handle: RePEc:eee:chsofr:v:94:y:2017:i:c:p:75-79
    DOI: 10.1016/j.chaos.2016.11.010
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    References listed on IDEAS

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    1. Salhoumi, A. & Galenko, P.K., 2016. "Gibbs–Thomson condition for the rapidly moving interface in a binary system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 161-171.
    2. Wazwaz, Abdul-Majid, 2008. "The extended tanh method for new compact and noncompact solutions for the KP–BBM and the ZK–BBM equations," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1505-1516.
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    Cited by:

    1. Liu, Hong-Zhun, 2022. "A modification to the first integral method and its applications," Applied Mathematics and Computation, Elsevier, vol. 419(C).

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