Abstract
Fully nonlinear electron-acoustic (EA) structures are studied in the presence of relativistic degeneracy pressure attributing to electron species in a degenerate plasma. The plasma is taken as a collisionless and unmagnetized, containing mobile cool electrons, inertialess hot electrons and static ions. The fluid equations for such a plasma are incorporated and solved together by using the charge-neutrality hypothesis and diagonalization matrix technique obtaining the characteristic wave equations in the form of inviscid Burgers' equations. Negative solitary structures are found in the form of potential profiles, which can be developed into nonstationary shocklets, greatly affected by the weak and strong relativistic degenerate densities. The structures are not only modified by the temporal evolution but also by thermal correction parameter. Moreover, the application of Taylor expansion to the eigenvalue may lead to the derivation of nonlinear phase and shock speeds, depending significantly on the electrostatic potential and other plasma parameters. The present findings are important to understand solitary and shocklet structures in dense plasmas, where both cool and hot electrons are regarded as the relativistic and degenerate species.