Nature

Exact solutions for nonlinear partial differential equations via a fusion of classical methods and innovative approaches

This paper presents a new approach for finding exact solutions to certain classes of nonlinear partial differential equations (NLPDEs) by combining the variation of parameters method with classical ...
Nature

High accuracy solutions for the Pochhammer–Chree equation in elastic media

This study investigates the nonlinear Pochhammer–Chree equation, a model crucial for understanding wave propagation in elastic rods, through the application of the Khater III method. The research aims ...
Phys.org

Mathematician discusses solving a seemingly unsolvable equation

After 10 years, Prof. Raimar Wulkenhaar from the University of Münster's Mathematical Institute and his colleague Dr. Erik Panzer from the University of Oxford have solved a mathematical equation ...
Quanta Magazine

Using AI, Mathematicians Find Hidden Glitches in Fluid Equations

Nearly 200 years ago, the physicists Claude-Louis Navier and George Gabriel Stokes put the finishing touches on a set of equations that describe how fluids swirl. And for nearly 200 years, the ...