Controversy on a dispersion relation for MHD waves

Abstract

Kumar et al. (2006) obtained a fifth order polynomial in $ω$ for the dispersion relation and pointed out that the calculations preformed by Porter et al. (1994) and by Dwivedi & Pandey (2003) seem to be in error, as they obtained a sixth order polynomial. The energy equation of Dwivedi & Pandey (2003) was dimensionally wrong. Dwivedi & Pandey (2006) corrected the energy equation and still claimed that the dispersion relation must be a sixth order polynomial. The equations (11) $-$ (19) of Dwivedi & Pandey (2006) and the equations (24) $-$ (32) Kumar et al. (2006) are the same. This fact has been expressed by Kumar et al. (2006) themselves. Even then they tried to show this set of equations on one side gives the sixth order polynomial as they got; on the other side, the same set of equations gives the fifth order polynomial as Kumar et al. (2006) obtained. The situation appears to be non-scientific, as the system of equations is a linear one. These are simple algebraic equations where the variables are to be eliminated. However, it is a matter of surprise that by solving these equations, two scientific groups are getting polynomials of different degrees. In the present discussion, we have attempted to short out this discrepancy.