Explicit solutions to the nonlinear VK system by the generalized separation of variables method*

The von Karman (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.

Automated summary

The combination of symmetry integration and separation of variables method is used to handle the von Karman system, resulting in new types of explicit solutions to the nonlinear system. Furthermore, exact solutions to a nonlinear ordinary differential equation system are investigated using the complete classification method, leading to the presentation of explicit solutions to the VK system.