The dispersionless Veselov–Novikov equation: symmetries, exact solutions, and conservation laws-Reference-Cited by-同舟云学术

The dispersionless Veselov–Novikov equation: symmetries, exact solutions, and conservation laws

Published:2021-06-18 Issue:3 Volume:11 Page:
ISSN:1664-2368
Container-title:Analysis and Mathematical Physics
language:en
Short-container-title:Anal.Math.Phys.

Author:

Morozov Oleg I.^ORCID,Chang Jen-Hsu

Abstract

AbstractWe study symmetries, invariant solutions, and conservation laws for the dispersionless Veselov–Novikov equation. The emphasis is placed on cases when the odes involved in description of the invariant solutions are integrable by quadratures. Then we find some non-invariant solutions, in particular, solutions that are polynomials of an arbitrary degree

$$N \ge 3$$

N ≥ 3 with respect to the spatial variables. Finally we compute all conservation laws that are associated to cosymmetries of second order.

Publisher

Springer Science and Business Media LLC

Subject

Mathematical Physics,Algebra and Number Theory,Analysis

Link

https://link.springer.com/content/pdf/10.1007/s13324-021-00563-8.pdf

Reference26 articles.

1. Baran, H., Marvan, M.: Jets: A software for differential calculus on jet spaces and diffieties. Available on-line at http://jets.math.slu.cz

2. Bogdanov, L.V., Konopelchenko, B.G., Moro, A.: Symmetry constraints for real dispersionless Veselov-Novikov equation. J. Math. Sci. 136(6), 4411–4418 (2006)

3. Chebyshev, P.L.: (Tchebychef). Sur l’intégration des différentielles irrationelles. Journal de mathématiques pures at appliquées. I. serie, XVIII (1853), 87-111, Œuvres T. I, pp. 142–168, Reprint. Chelsea, N.Y., (1961)

4. Chebyshev, P.L.: (Tchebychef). Sur l’intégration des différentielles les plus simples parmi celles qui contiennent une racine cubique. Matem. Sbornik II (1867), 71–78, Œuvres T. II, pp. 41–47, Reprint. Chelsea, N.Y., (1961)

5. Clarkson, P.A.: Nonclassical symmetry reductions of nonlinear partial differential equations. Math. Comput. Model. 18, 45–68 (1993)

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