該期刊發表關于非線性雙曲線問題和相關主題的原始研究論文，數學和/或物理興趣。具體而言，它邀請了關于雙曲守恒定律和數學物理中出現的雙曲偏微分方程的理論和數值分析的論文。期刊歡迎以下方面的貢獻：非線性雙曲守恒定律系統理論，解決了一個或多個空間維度中解的適定性和定性行為問題。數學物理的雙曲微分方程，如廣義相對論的愛因斯坦方程，狄拉克方程，麥克斯韋方程，相對論流體模型等。洛倫茲幾何，特別是滿足愛因斯坦方程的時空的全局幾何和因果理論方面。連續體物理中出現的非線性雙曲系統，如：流體動力學的雙曲線模型，跨音速流的混合模型等。由有限速度現象主導（但不是唯一驅動）的一般問題，例如雙曲線系統的耗散和色散擾動，以及來自統計力學和與流體動力學方程的推導相關的其他概率模型的模型。雙曲型方程數值方法的收斂性分析：有限差分格式，有限體積格式等。該期刊旨在為目前正在非常活躍的非線性雙曲線問題領域工作的研究人員提供一個論壇，并且還將作為此類研究用戶的信息來源。提交稿件的長度沒有先驗限制，甚至可能會發表長篇論文。

This journal publishes original research papers on nonlinear hyperbolic problems and related topics, of mathematical and/or physical interest. Specifically, it invites papers on the theory and numerical analysis of hyperbolic conservation laws and of hyperbolic partial differential equations arising in mathematical physics. The Journal welcomes contributions in:Theory of nonlinear hyperbolic systems of conservation laws, addressing the issues of well-posedness and qualitative behavior of solutions, in one or several space dimensions.Hyperbolic differential equations of mathematical physics, such as the Einstein equations of general relativity, Dirac equations, Maxwell equations, relativistic fluid models, etc.Lorentzian geometry, particularly global geometric and causal theoretic aspects of spacetimes satisfying the Einstein equations.Nonlinear hyperbolic systems arising in continuum physics such as: hyperbolic models of fluid dynamics, mixed models of transonic flows, etc.General problems that are dominated (but not exclusively driven) by finite speed phenomena, such as dissipative and dispersive perturbations of hyperbolic systems, and models from statistical mechanics and other probabilistic models relevant to the derivation of fluid dynamical equations.Convergence analysis of numerical methods for hyperbolic equations: finite difference schemes, finite volumes schemes, etc.The Journal aims to provide a forum for the community of researchers who are currently working in the very active area of nonlinear hyperbolic problems, and will also serve as a source of information for the users of such research.There is no a priori limitation on the length of submitted manuscripts, and even long papers may be published.