A Saddle-Node Bifurcation Scenario for Disappearance of Nonlinear Electrostatic Waves in an Ultra-Relativistic Degenerate Dense Plasma

Abstract

The birth or destruction of electrostatic excitations is investigated in an ultra-relativistic degenerate dense dusty plasma by the saddle-node bifurcation scenario. An abstract form of bifurcation is derived which captures the main features of traveling wave solutions for various regions in the parameter space of plasma number density. We show that a sudden disappearance of solitary and supernonlinear periodic waves occurs at the critical point of saddle-node bifurcation. For a range of ion number density and dust concentration, we obtain the critical values of bifurcation and different existence domains of stability region. The numerical phase portrait analysis is also performed to examine the coexistence of solitary waves, nonlinear periodic, and supernonlinear periodic waves for different conditions. We further derive analytically the conditions with respect to the model parameters that give rise to both polarities of solitary waves. It is found that the amplitude of localized structures decreases with the increase in the plasma number density. Our results could be applicable for astrophysical objects with high density matter such as white dwarfs and neutron stars.