Symmetries and conservation laws for the Karczewska--Rozmej--Rutkowski--Infeld equation
A. Sergyeyev, R.F. Vitolo
TL;DR
This paper thoroughly analyzes the symmetries and conservation laws of a fifth-order shallow water wave equation, revealing its lack of generalized symmetries and non-integrability.
Contribution
It provides a complete classification of symmetries and conservation laws for the Karczewska--Rozmej--Rutkowski--Infeld equation, establishing its non-integrability.
Findings
No genuinely generalized symmetries found
Equation is not symmetry integrable
Complete description of conservation laws provided
Abstract
We give a complete description of generalized symmetries and local conservation laws for the fifth-order Karczewska--Rozmej--Rutkowski--Infeld equation describing shallow water waves in a channel with variable depth. In particular, we show that this equation has no genuinely generalized symmetries and thus is not symmetry integrable.
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