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      https://www.ias.ac.in/article/fulltext/pram/095/0134

    • Keywords

       

      Extended Sawada–Kotera equation; extended Lax equation; Hirota bilinear method; propagation angle; lump wave; breather wave; cnoidal periodic waves

    • Abstract

       

      In this paper, we investigate two extended higher-order KdV models (i.e., the extended Sawada–Kotera equation and the extended Lax equation), which can successfully describe propagation of dimly nonlinear long waves in fluids and ion-acoustic waves in harmonic sparklers. First, we present a general formula of multisoliton solutions of the two models. We then build the interaction solutions in terms of hyperbolic and sinusoidal functions by using multisoliton solutions with appropriate complex conjugate parameters controlling the phase shifts, propagation direction and energies of the waves. In particular, we present their collision solutions in the identical plane with different parametric constraints, which degenerate to the line rogue waves, x-shaped rogue waves, cnoidal periodic waves, interactions of rogue and bell waves, line breather and double breather waves. The dynamical characteristics of the wave solutions are shown graphically by choosing some special parameter values.

    • Author Affiliations

       

      ZILLUR RAHMAN1 2 M ZULFIKAR ALI2 HARUN-OR-ROSHID2 3 MOHAMMAD SAFI ULLAH1 2 XIAO-YONG WEN4

      1. Department of Mathematics, Comilla University, Cumilla 3506, Bangladesh
      2. Department of Mathematics, Rajshahi University, Rajshahi 6205, Bangladesh
      3. Department of Mathematics, Pabna University of Science and Technology, Pabna 6600, Bangladesh
      4. School of Applied Science, Beijing Information Science and Technology University, Beijng 100192, People’s Republic of China
    • Dates

       
  • Pramana – Journal of Physics | News

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