| Abstract: |
| Several years ago, two important papers [1,2] were published on common errors that are often made in investigations of finding exact solutions to nonlinear partial differential equations. These papers were motivated by a large (and still growing) number of publications
appearing in the literature in which basic errors were repeated concerning correctness, generality, and novelty of exact solutions, as well as methods for their construction, and proper citation of previous work.
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In the past decade, a similar situation has arisen with investigations of finding conservation laws of nonlinear partial differential equations. I will point several common errors that are made in the literature on this topic. The errors deal with generality and novelty of conservation laws, as well as methods for their construction [3] and proper citation of previous work [4].
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[1] N.A. Kudryashov,
Seven common errors in finding exact solutions of nonlinear differential equations,
Commun. Nonlinear Sci. Numer. Simulat. 14, pp. 3507--3529 (2009).
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[2] R.O. Popovych, O.O. Vaneeva,
More common errors in finding exact solutions of nonlinear differential equations,
Commun. Nonlinear Sci. Numer. Simul. 15, pp. 3887--3899 (2010).
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[3] S.C. Anco,
Generalization of Noether`s theorem in modern form to non-variational partial differential equations,
In: Recent progress and Modern Challenges in Applied Mathematics, Modeling and Computational Science, Fields Institute Communications 79 (2017).
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[4] S.C. Anco,
On the incompleteness of Ibragimov`s conservation law theorem and its equivalence to a standard formula using symmetries and adjoint-symmetries,
Symmetry 9(3), 33 (2017). |
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