Compressive and rarefactive DIA solitons beyond the KdV limit

The modified Gardner equation (MGE), showing the existence of compressive and rarefactive dust-ion-acoustic (DIA) solitons in a nonplanar dusty plasma (containing inertial ions, Boltzmann electrons, and negatively charged stationary dust) beyond the KdV Korteweg-de Vries (KdV) limit, is derived and numerically solved. The basic features of the compressive and rarefactive cylindrical and spherical DIA solitons, which are found to exist beyond the KdV limit, i.e., exist for μ ∼ 2/3 (where μ = Znnd0/ni0, zd is the number of electrons residing onto the dust grain surface, nd0(ni0) is the dust (ion) number density at equilibrium, and μ ∼ 2/3 means that μ is not equal to 2/3, but it is around 2/3) are identified. These solitons (which can be referred to as DIA Gardner solitons (DIA-GSs)) are completely different from the KdV solitons because μ = 2/3 corresponds to the vanishing of the nonlinear coefficient of the KdV equation, and μ ∼ 2/3 corresponds to extremely large amplitude KdV solitons for which the validity of the reductive perturbation method breaks down. It is also shown that the properties of the nonplanar (cylindrical and spherical) DIA-GSs are significantly different from those of the one dimensional planar ones.