The propagation of ion-acoustic (IA) solitary and rogue waves is investigated in a two-dimensional ultrarelativistic degenerate warm dense plasma. By using the reductive perturbation technique, the cylindrical Kadomtsev–Petviashvili (KP) equation is derived, which can be further transformed into a Korteweg–de Vries (KdV) equation. The latter admits a solitary wave solution. However, when the frequency of the carrier wave is much smaller than the ion plasma frequency, the KdV equation can be transferred to a nonlinear Schrödinger equation to study the nonlinear evolution of modulationally unstable modified IA wavepackets. The propagation characteristics of the IA solitary and rogue waves are strongly influenced by the variation of different plasma parameters in an ultrarelativistic degenerate dense plasma. The present results might be helpful to understand the nonlinear electrostatic excitations in astrophysical degenerate dense plasmas.
Received 22 April 2013Accepted 03 June 2013Published online 08 July 2013
One of the authors (Ata-ur-Rahman) gratefully acknowledges the financial support of Higher Education Commission (HEC) of Pakistan through Indigenous 5000 Ph.D Scholarship Scheme. W.M.M. thanks the sponsorship provided by the Alexander von Humboldt Foundation (Bonn, Germany) in the framework of the Research Group Linkage Programme funded by the respective Federal Ministry.
Article outline: I. INTRODUCTION II. BASIC EQUATIONS AND FORMULATIONS III. ROGUE WAVE PROPAGATION IV. RESULTS AND DISCUSSION