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- Title
The Zakharov–Shabat Spectral Problem for Complexification and Perturbation of the Korteweg–de Vries Equation.
- Authors
Redkina, Tatyana V.; Zakinyan, Arthur R.; Zakinyan, Robert G.
- Abstract
In this paper we consider examples of complex expansion (cKdV) and perturbation (pKdV) of the Korteweg–de Vries equation (KdV) and show that these equations have a representation in the form of the zero-curvature equation. In this case, we use the Lie algebra of 4-dimensional quadratic nilpotent matrices. Moreover, it is shown that the simplest possible matrix representation of this algebra leads to the possibility of constructing a countable number of conservation laws for these equations.
- Subjects
KORTEWEG-de Vries equation; CONSERVATION laws (Mathematics); REPRESENTATIONS of algebras; MATRICES (Mathematics); LIE algebras; CONSERVATION laws (Physics)
- Publication
Axioms (2075-1680), 2023, Vol 12, Issue 7, p703
- ISSN
2075-1680
- Publication type
Article
- DOI
10.3390/axioms12070703