22 citations · 60 across the 11 of their papers we have counts for
11 papers
On a class of 3D second-order integrable Lagrangians and their dispersive deformations
Lingling Xue, E. V. Ferapontov, M. V. Pavlov
We investigate integrability of Euler-Lagrange equations associated with 3D second-order Lagrangians of the form \begin{equation*} \int f(u_{xy},u_{xt},u_{yt})\ \text{d}x\text{d}y\…
Lagrangian formulation of the Darboux system
Lingling Xue, E. V. Ferapontov, M. V. Pavlov
The classical Darboux system governing rotation coefficients of three-dimensional metrics of diagonal curvature possesses an equivalent formulation as a sixth-order PDE for a scala…
Bäcklund-Darboux Transformations for Super KdV Type Equations
Lingling Xue, Shasha Wang, Qing Ping Liu
By introducing a Miura transformation, we derive a generalized super modified Korteweg-de Vries (gsmKdV) equation from the generalized super KdV (gsKdV) equation. It is demonstrate…
A class of reductions of the two-component KP hierarchy and the Hirota-Ohta system
L. V. Bogdanov, Lingling Xue
We introduce a class of reductions of the two-component KP hierarchy, which includes the Hirota-Ohta system hierarchy. The description of the reduced hierarchies is based on the Hi…
Second-order integrable Lagrangians and WDVV equations
Evgeny V. Ferapontov, Maxim V. Pavlov, Lingling Xue
We investigate integrability of Euler-Lagrange equations associated with 2D second-order Lagrangians of the form \begin{equation*} \int f(u_{xx},u_{xy},u_{yy})\ dxdy. \end{equation…
Quasilinear systems of Jordan block type and the mKP hierarchy
Lingling Xue, E. V. Ferapontov
We demonstrate that commuting quasilinear systems of Jordan block type are parametrised by solutions of the modified KP hierarchy. Systems of this form naturally occur as hydrodyna…
Supersymmetric Sawada-Kotera Equation: Bäcklund-Darboux Transformations and Applications
Hui Mao, Q. P. Liu, Lingling Xue
In this paper, we construct a Darboux transformation and the related Bäcklund transformation for the supersymmetric Sawada-Kotera (SSK) equation. The associated nonlinear superposi…
Darboux transformations for supersymmetric two-boson equation
Xiao-Xing Niu, Q. P. Liu, Lingling Xue
In this paper we construct Darboux transformations for the supersymmetric Two-boson equation. Two Darboux transformations and associated Bäcklund transformations are presented. For…
A supersymmetric AKNS problem and its Darboux-Bäcklund transformations and discrete systems
Lingling Xue, Q. P. Liu
In this paper, we consider a supersymmetric AKNS spectral problem. Two elementary and a binary Darboux transformations are constructed. By means of reductions, Darboux and Bäcklund…
Bäcklund-Darboux Transformations and Discretizations of Super KdV Equation
Ling-Ling Xue, Qing Ping Liu
For a generalized super KdV equation, three Darboux transformations and the corresponding Bäcklund transformations are constructed. The compatibility of these Darboux transformatio…
Supersymmetric KdV equation: Darboux transformation and discrete systems
Ling-Ling Xue, D. Levi, Q. P. Liu
For the supersymmetric KdV equation, a proper Darboux transformation is presented. This Darboux transformation leads to the Bäcklund transformation found early by Liu and Xie \cite…