Explicit solutions to the nonlinear VK system by the generalized separation of variables method* *This work is supported by the Natural Science Foundation of Shandong Province under Grant No. ZR2020MA011, the high-level personnel foundation of Liaocheng University under grant Nos. 318050087 and 318011613.

Abstract

The von Kármán (VK) system is of great importance in mechanics and physical applications, but it is difficult to cope with explicit solutions to such a nonlinear partial differential equation (NLPDE) system. In this paper, we develop the combination of symmetry integration and separation of variables method (SVM) to deal with this NLPDE system, some new types of explicit solutions to the nonlinear system are obtained. Moreover, by the complete classification method, we investigate exact solutions to a nonlinear ordinary differential equation (NLODE) system, so the explicit solutions to the VK system are presented.