A rigorous theoretical study has been made on obliquely propagating dust-acoustic solitary waves (OPDASWs) and cnoidal waves in a dense degenerate dusty plasma medium in the presence of temperature degenerate trapped electrons and κ−nonthermal ion population. A reductive perturbation technique has been adopted to obtain the Zakharov-Kuznetsov (ZK) equation and the modified ZK (mZK) equation. The solitary wave solutions of ZK and mZK equations are obtained to analyse the characteristics of solitary waves in such a plasma. The Jacobi (cn) elliptic periodic wave solution for mZK is also derived to analyse the nature of dust acoustic travelling wave. The different plasma parameters (e.g., electron-to-dust number density via δ, ions nonthermality via κ, temperature effect of degenerate trapped electrons via T, etc.) are seen to have significant inluence on the propagation nature of OPDASWs. The applications of results may be useful to explain/understand the nature of solitary waves in different ultra-dense astrophysical environments (such as neutron stars, white dwarfs etc. [1, 2]) and also in experiments involve the interaction of laser and solid density plasma and inertial confinement fusion, [3, 4] in which the relativistic effects play major role.
