Nonlocally related systems, nonlocal symmetry reductions and exact solutions for one-dimensional macroscopic production model
Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, India
Accepted: 11 June 2020
Published online: 22 June 2020
We perform the classification of nonlocal symmetries and obtain some exact solutions to the system of nonlinear partial differential equations (PDEs), which describe a one-dimensional macroscopic production model. We obtain infinitely many nonlocal conservation laws, which lead to producing new potential systems. Further, we construct a tree of nonlocally related PDE systems using local conservation laws and symmetry-based method. The governing system of PDEs admits nonlocal symmetries from potential systems as well as inverse potential systems. Using these nonlocal symmetries, we obtain some implicit solutions and one arbitrary family of solutions that can be reduced to explicit form by some particular choice of the arbitrary function. Further, the physical behavior of different explicit solutions is shown graphically.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020