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Nonlocally related systems, nonlocal symmetry reductions and exact solutions for one-dimensional macroscopic production model

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Abstract

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.

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Acknowledgements

Authors would like to convey their gratitude to reviewers for their fruitful comments and suggestions. We are grateful to Professor G. W. Bluman (Professor Emeritus, UBC, Canada) for his valuable suggestions and discussion to improve the article. The first author is highly thankful to Ministry of Human Resource Development, Government of India, for the institute fellowship (Grant No. IIT/ACAD/PGS & R/F.II/2/16MA90J04).

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  1. Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, India

    Subhankar Sil & T. Raja Sekhar

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  1. Subhankar Sil
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  2. T. Raja Sekhar
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Correspondence to T. Raja Sekhar.

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Sil, S., Raja Sekhar, T. Nonlocally related systems, nonlocal symmetry reductions and exact solutions for one-dimensional macroscopic production model. Eur. Phys. J. Plus 135, 514 (2020). https://doi.org/10.1140/epjp/s13360-020-00530-5

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