Compactons in discrete nonlinear Klein–Gordon models

In this short communication we study compactons in the setting of discrete nonlinear Klein–Gordon (DNKG) chains. The temporal and spatial dependences of the solutions are separated resulting in an array of coupled nonlinear algebraic equations for the spatial dependence and an ordinary differential equation for the temporal dependence. The corresponding equations are studied and their potential for supporting exact discrete solutions with compact support is identified. Finally, a particular set of KG nonlinearities of relevance to applications is studied, its discrete compacton solutions are obtained and their stability properties are examined.