Click here to view fulltext PDF

Permanent link:
https://www.ias.ac.in/article/fulltext/pram/088/02/0028

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

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.

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

Published

16 February 2017

Manuscript received

22 January 2016

Manuscript revised

25 June 2016

Accepted

20 July 2016

Early published

4 January 2017