Pramana

, 88:28 | Cite as

Solitons, compactons and undular bores in Benjamin–Bona–Mahony-like systems

  • APARNA SAHA
  • B TALUKDAR
  • UMAPADA DAS
  • SUPRIYA CHATTERJEE
Article
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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 is linear 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.

Keywords

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

PACS Nos

02.30.Gp 02.30.Hq 02.30.Jr 
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Notes

Acknowledgement

The authors would like to thank Drs Sk Golam Ali and Amitava Choudhuri for their kind interest in this work.

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Copyright information

© Indian Academy of Sciences 2017

Authors and Affiliations

  • APARNA SAHA
    • 1
  • B TALUKDAR
    • 1
  • UMAPADA DAS
    • 2
  • SUPRIYA CHATTERJEE
    • 3
  1. 1.Department of PhysicsVisva Bharati UniversitySantiniketanIndia
  2. 2.Department of PhysicsAbhedananda CollegeSainthiaIndia
  3. 3.Department of PhysicsBidhannagar CollegeKolkataIndia

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