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    • Keywords

       

      Benjamin–Bona–Mahony-like equations; travelling wave solutions; solitons; compactons; dissipation; undular bores; shock waves.

    • Abstract

       

      We examine the effect of dissipation on travelling waves in nonlinear dispersive systems modelled by Benjamin–Bona–Mahony (BBM)-like equations. In the absence of dissipation, the BBM-like equations are found to support soliton and compacton/anticompacton solutions depending on whether the dispersive term islinear or nonlinear. We study the influence of increasing nonlinearity of the medium on the soliton and compacton dynamics. The dissipative effect is found to convert the solitons either to undular bores or to shock-like waves depending on the degree of nonlinearity of the equations. The anticompacton solutions are also transformed to undular bores by the effect of dissipation. But the compactons tend to vanish due to viscous effects. The local oscillatory structures behind the bores and/or shock-like waves in the case of solitons and anticompactons are found to depend sensitively both on the coefficient of viscosity and solution of the unperturbed problem.

    • Author Affiliations

       

      APARNA SAHA1 B TALUKDAR1 UMAPADA DAS2 SUPRIYA CHATTERJEE3

      1. Department of Physics, Visva Bharati University, Santiniketan 731 235, India
      2. Department of Physics, Abhedananda College, Sainthia 731 234, India
      3. Department of Physics, Bidhannagar College, EB-2, Sector-1, Salt Lake, Kolkata 700 064, India
    • Dates

       
  • Pramana – Journal of Physics | News

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