Applications of homotopy method on nonlinear partial differential equations

Homotopy method is being used to explore nonlinear partial differential equation system arising from engineering and physics. This new approach is used to compute multiple solutions of nonlinear PDEs and yields the discretized polynomial systems, which involve thousands of variables. This method can also handle the singularities. This talk will cover the recent progress on nonlinear PDEs such as free boundary problem and hyperbolic conservation law problem.