Journal
RUSSIAN MATHEMATICAL SURVEYS
Volume 68, Issue 5, Pages 889-921Publisher
TURPION LTD
DOI: 10.1070/RM2013v068n05ABEH004860
Keywords
differential equations; nonlinear self-adjointness; conservation laws; exact solutions
Categories
Funding
- Government of the Russian Federation [11.G34.31.0042]
Ask authors/readers for more resources
The method of nonlinear self-adjointness, which was recently developed by the first author, gives a generalization of Noether's theorem. This new method significantly extends approaches to constructing conservation laws associated with symmetries, since it does not require the existence of a Lagrangian. In particular, it can be applied to any linear equations and any nonlinear equations that possess at least one local conservation law. The present paper provides a brief survey of results on conservation laws which have been obtained by this method and published mostly in recent preprints of the authors, along with a method for constructing exact solutions of systems of partial differential equations with the use of conservation laws. In most cases the solutions obtained by the method of conservation laws cannot be found as invariant or partially invariant solutions.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available