In recent time, by working in a plane with the metric associated with wave equation (the Special Relativity non-definite quadratic form), a complete formalization of space-time trigonometry and a Cauchy-like integral formula have been obtained. In this paper the concept that the solution of a mathematical problem is simplified by using a "mathematics" with the symmetries of the problem, actuates us for studying the wave equation (in particular "the initial values problem") in a plane where the geometry is the one "generated" by the wave equation itself. In this way, following a classical approach, we point out the well known differences with respect to Laplace equation notwithstanding their formal equivalence (partial differential equations of second order with constant coefficients) and also show that the same conditions stated for Laplace equation allow us to find a new solution. In particular taking as "initial data" for the wave equation an arbitrary function given on an arm of an equilateral hyperbola, a "Poisson-like" integral formula holds.
An integral representation for the resolvent kernel with magnetic fields on the hyperbolic plane and applications to time dependent Schrödinger equations
A Family of Berndt-Type Integrals and Associated Barnes Multiple Zeta Functions
School of Mathematics and Statistics, Anhui Normal University（安徽师范大学数学与统计学院）；School of Mathematics and Computational Science, Xiangtan University（湘潭大学数学与计算科学学院）
Beijing Institute of Mathematical Sciences and Applications（北京国际数学研究中心）；Laboratory of Theoretical Physics, JINR（约飞联合核子研究所理论物理实验室）；Yerevan Physics Institute（埃里安物理研究所）；National Research University Higher School of Economics（国立研究大学高等经济大学）
Triple Hodge integrals and constant Poisson brackets for rank-one Dubrovin-Zhang hierarchies
Korteweg–de Vriesinstituut voor Wiskunde, Universiteit van Amsterdam（阿姆斯特丹大学科特韦格-德弗里斯数学研究所）；Université Bourgogne Europe, CNRS, IMB UMR 5584（勃艮第欧洲大学，法国国家科学研究中心，IMB UMR 5584）
