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Construction of the soliton solutions and modulation instability analysis for the Mel’nikov system

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  • Kumar, Vineesh
  • Patel, Arvind

Abstract

This paper addresses the soliton solutions of the Mel’nikov system by the complex amplitude ansatz method and the He’s variational principle. The bright, anti-bright, dark, anti-dark, kink, anti-kink, bell-shaped, breather and homoclinic orbits are obtained as different possible solutions of the Mel’nikov system by the two methods. The solutions and their dynamical behaviour captured by the two methods are discussed. The solutions contain enough number of free physical parameters. These solutions give a better explanation of the associated physical phenomena. The modulation instability analysis of the steady-state solutions of the Mel’nikov system is investigated. This investigation has revealed that the Mel’nikov system is stable against small perturbation for a certain range of perturbation wave numbers. Apart from this, these solutions also help in validating the amount of accuracy in the numerical solutions and to perform the stability analysis further.

Suggested Citation

  • Kumar, Vineesh & Patel, Arvind, 2020. "Construction of the soliton solutions and modulation instability analysis for the Mel’nikov system," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
  • Handle: RePEc:eee:chsofr:v:140:y:2020:i:c:s0960077920305555
    DOI: 10.1016/j.chaos.2020.110159
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    References listed on IDEAS

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    1. Wazwaz, Abdul-Majid, 2005. "Generalized forms of the phi-four equation with compactons, solitons and periodic solutions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 69(5), pages 580-588.
    2. Porsezian, K. & Murali, R. & Malomed, Boris A. & Ganapathy, R., 2009. "Modulational instability in linearly coupled complex cubic–quintic Ginzburg–Landau equations," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1907-1913.
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