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.

在存在温度简并俘获电子和κ -非热离子群的情况下，已经对在致密简并尘埃等离子体介质中倾斜传播的尘埃声孤立波 (OPDASW) 和 cnoidal 波进行了严格的理论研究。已采用还原扰动技术来获得 Zakharov-Kuznetsov (ZK) 方程和修改后的 ZK (mZK) 方程。得到ZK和mZK方程的孤立波解来分析等离子体中孤立波的特性。还推导出 mZK 的 Jacobi (cn) 椭圆周期波解，以分析尘埃声行波的性质。不同的等离子体参数（例如，通过δ 的电子对尘埃数密度，通过κ 的离子非热性，通过T的简并俘获电子的温度效应等）被认为对 OPDASW 的传播性质有显着影响。结果的应用可能有助于解释/理解不同超高密度天体物理环境（如中子星、白矮星等）中孤立波的性质 [1, 2]），也可用于涉及激光和固体相互作用的实验密度等离子体和惯性约束聚变[3, 4]，其中相对论效应起主要作用。