Veronese webs and nonlinear PDEs
TLDR
In this article, the authors show relations of Veronese three-dimensional webs to several other integrable equations, deform these equations preserving integrability via a dispersionless Lax pair and compute the corresponding contact symmetries, Backlund transformations and Einstein-Weyl structures.About:
This article is published in Journal of Geometry and Physics.The article was published on 2017-05-01 and is currently open access. It has received 18 citations till now. The article focuses on the topics: Dispersionless equation & Lax pair.read more
Citations
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Lie symmetry reductions and group invariant solutions of (2 + 1)-dimensional modified Veronese web equation
Sachin Kumar,Amit Kumar +1 more
TL;DR: In this article, the authors applied the Lie symmetry method to compute group invariant solutions for the modified Veronese web (mVw) equation and obtained its infinitesimals, commutation table of Lie algebra, symmetry reductions and closed form analytical solutions.
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Infinitely many nonlocal conservation laws for the ABC equation with \(A+B+C\ne 0\)
TL;DR: In this article, an infinite hierarchy of nonlocal conservation laws for the ABC equation was constructed using a nonisospectral Lax pair, where A, B, C are nonzero constants.
Journal ArticleDOI
Infinitely many nonlocal conservation laws for the $ABC$ equation with $A+B+C\neq 0$
TL;DR: In this paper, an infinite hierarchy of nonlocal conservation laws for the ABC equation was constructed using a nonisospectral Lax pair and the method of proof of nontriviality of the conservation laws under study is quite general and can be applied to many other integrable multidimensional systems.
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Nonlocal symmetries, conservation laws, and recursion operators of the Veronese web equation
TL;DR: In this paper, the Veronese web equation is studied and two infinite series of nonlocal conservation laws are constructed using the isospectral Lax pair, and the Lie algebras of corresponding nonlocal symmetries are described.
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On deformations of the dispersionless Hirota equation
TL;DR: In this article, the authors show that simple geometric constructions on the associated twistor space lead to deformations of the Hirota equation that have been introduced recently by B.Kruglikov and A.Panasyuk.
References
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Book ChapterDOI
Complex manifolds and Einstein’s equations
TL;DR: In this paper, a generalization of Penrose's twistor theory based on the geometry of rational curves in complex manifolds is presented, in the three simplest cases, of a system of differential equations closely connected with Einstein's equations.
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Integrable hydrodynamic chains
TL;DR: In this article, a new approach for derivation of Benney-type moment chains and integrable hydrodynamic type systems is presented, and new integrably hydrodynamical chains are constructed; all their hydroynamical reductions are described and integrated.
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Minitwistor spaces and Einstein-Weyl spaces
P E Jones,K. P. Tod +1 more
TL;DR: In this article, the Hitchin correspondence between minitwistor spaces and Einstein-Weyl spaces was shown to be equivalent to the Penrose correspondence between twistor spaces and spacetimes with anti-self-dual Weyl tensors.