72 citations · 436 across the 25 of their papers we have counts for
25 papers
Global Results on the Classification of Two-Component Integrable Evolutionary Systems
Alexander V. Mikhailov, Vladimir Novikov, Jing Ping Wang
We derive necessary and sufficient integrability conditions for two-component polynomial evolutionary systems of odd order in dimensions. Integrable systems are members of…
Algebraic quantisation approach to integrable differential-difference equations
Sylvain Carpentier, Alexander V. Mikhailov, Jing Ping Wang
We develop an algebraic quantisation approach, based on quantisation ideals, and apply it to integrable non-Abelian differential--difference equations. We show that the Toda hierar…
Integrability of Nonabelian Differential-Difference Equations: the Symmetry Approach
Vladimir Novikov, Jing Ping Wang
We propose a novel approach to tackle integrability problem for evolutionary differential-difference equations (DEs) on free associative algebras, also referred to as nonabelian…
Hamiltonians for the quantised Volterra hierarchy
Sylvain Carpentier, Alexander V. Mikhailov, Jing Ping Wang
This paper builds upon our recent work, published in Lett. Math. Phys., 112: 94, 2022, where we established that the integrable Volterra lattice on a free associative algebra and t…
Hamiltonian and recursion operators for a discrete analogue of the Kaup-Kupershmidt equation
Edoardo Peroni, Jing Ping Wang
In this paper we study the algebraic properties of a new integrable differential-difference equation. This equation can be seen as a deformation of the modified Narita-Itoh-Bogoyav…
Quantisations of the Volterra hierarchy
Sylvain Carpentier, Alexander V. Mikhailov, Jing Ping Wang
In this paper we explore a recently emerged approach to the problem of quantisation based on the notion of quantisation ideals. We explicitly prove that the nonabelian Volterra tog…
Perturbative Symmetry Approach for Differential-Difference Equations
A. V. Mikhailov, V. S. Novikov, J. P. Wang
We propose a new method for solution of the integrability problem for evolutionary differential-difference equations of arbitrary order. It enables us to produce necessary integrab…
Hamiltonian structures for integrable nonabelian difference equations
Matteo Casati, Jing Ping Wang
In this paper we extensively study the notion of Hamiltonian structure for nonabelian differential-difference systems, exploring the link between the different algebraic (in terms…
Generalizations of the short pulse equation
Andrew N. W. Hone, Vladimir Novikov, Jing Ping Wang
We classify integrable scalar polynomial partial differential equations of second order generalizing the short pulse equation.
Symbolic Representation and Classification of N=1 Supersymmetric Evolutionary Equations
Kai Tian, Jing Ping Wang
We extend the symbolic representation to the ring of N=1 supersymmetric differential polynomials, and demonstrate that operations on the ring, such as the super derivative, Frechet…
Wave fronts and cascades of soliton interactions in the periodic two dimensional Volterra system
Rhys Bury, Alexander V. Mikhailov, Jing Ping Wang
In the paper we develop the dressing method for the solution of the two-dimensional periodic Volterra system with a period N. We derive soliton solutions of arbitrary rank and…
Two-component generalizations of the Camassa-Holm equation
Andrew N. W. Hone, Vladimir Novikov, Jing Ping Wang
A classification of integrable two-component systems of non-evolutionary partial differential equations that are analogous to the Camassa-Holm equation is carried out via the pertu…
Darboux transformation for the vector sine-Gordon equation and integrable equations on a sphere
Alexander V. Mikhailov, Georgios Papamikos, Jing Ping Wang
We propose a method for construction of Darboux transformations, which is a new development of the dressing method for Lax operators invariant under a reduction group. We apply the…
Dressing method for the vector sine-Gordon equation and its soliton interactions
Alexander V. Mikhailov, Georgios Papamikos, Jing Ping Wang
In this paper, we develop the dressing method to study the exact solutions for the vector sine-Gordon equation. The explicit formulas for one kink and one breather are derived. The…
Representations of sl(2,C) in the BGG category O and master symmetries
Jing Ping Wang
In this paper, we first give a short account on the indecomposable sl(2,C) modules in the Bernstein-Gelfand-Gelfand (BGG) category O. We show these modules naturally arise for homo…
Darboux transformation with Dihedral reduction group
Alexander V. Mikhailov, Georgios Papamikos, Jing Ping Wang
We construct the Darboux transformation with Dihedral reduction group for the 2-dimensional generalisation of the periodic Volterra lattice. The resulting Backlund transformation c…
Darboux transformations and Recursion operators for differential--difference equations
Farbod Khanizadeh, Alexander V. Mikhailov, Jing Ping Wang
In this paper we review two concepts directly related to the Lax representations: Darboux transformations and Recursion operators for integrable systems. We then present an extensi…
Hamiltonian evolutions of twisted gons in $\RP^n$
Gloria Marí Beffa, Jing Ping Wang
In this paper we describe a well-chosen discrete moving frame and their associated invariants along projective polygons in $\RP^n$, and we use them to write explicit general expres…
Recursion operator of the Narita-Itoh-Bogoyavlensky lattice
Jing Ping Wang
We construct a recursion operator for the family of Narita-Itoh-Bogoyavlensky infinite lattice equations using its Lax presentation and present their mastersymmetries and bi-Hamilt…
A new recursion operator for the Viallet equation
Alexander V. Mikhailov, Jing Ping Wang
We present a new recursion and Hamiltonian operators for the Viallet equation. This new recursion operator and the recursion operator found in [Theoretical and Mathematical Physics…
Cosymmetries and Nijenhuis recursion operators for difference equations
Alexander V. Mikhailov, Jing Ping Wang, Pavlos Xenitidis
In this paper we discuss the concept of cosymmetries and co--recursion operators for difference equations and present a co--recursion operator for the Viallet equation. We also dis…
The Hunter-Saxton equation: remarkable structures of symmetries and conserved densities
Jing Ping Wang
In this paper, we present extraordinary algebraic and geometrical structures for the Hunter-Saxton equation: infinitely many commuting and non-commuting -independent higher or…
Recursion operators, conservation laws and integrability conditions for difference equations
Alexander V. Mikhailov, Jing Ping Wang, Pavlos Xenitidis
In this paper we make an attempt to give a consistent background and definitions suitable for the theory of integrable difference equations. We adapt a concept of recursion operato…
Lenard scheme for two dimensional periodic Volterra chain
Jing Ping Wang
We prove that for compatible weakly nonlocal Hamiltonian and symplectic operators, hierarchies of infinitely many commuting local symmetries and conservation laws can be generated…