982 citations · 1.8k across the 34 of their papers we have counts for
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Duality of positive and negative integrable hierarchies via relativistically invariant fields
S. Y. Lou, X. B. Hu, Q. P. Liu
It is shown that the relativistic invariance plays a key role in the study of integrable systems. Using the relativistically invariant sine-Gordon equation, the Tzitzeica equation,…
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…
Conservation laws of the generalized Riemann equations at
Binfang Gao, Kai Tain, Q. P. Liu +1
In this paper, we present infinitely many conserved densities satisfying particular conservation law for the generalized Riemann equations at . In the $N…
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…
Conservation laws and symmetries of Hunter-Saxton equation: revisited
Kai Tian, Q. P. Liu
Through a reciprocal transformation induced by the conservation law , the Hunter-Saxton (HS) equation $u_{xt} = 2uu_{2x} +…
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…
A four-component Camassa-Holm type hierarchy
Nianhua Li, Q. P. Liu, Z. Popowicz
We consider a 33 spectral problem which generates four-component CH type systems. The bi-Hamiltonian structure and infinitely many conserved quantities are constructed for…
High Order Solutions and Generalized Darboux Transformations of Derivative Schrödinger Equation
Boling Guo, Liming Ling, Q. P. Liu
By means of certain limit technique, two kinds of generalized Darboux transformations are constructed for the derivative nonlinear Schödinger equation (DNLS). These transformations…
A non-standard Lax formulation of the Harry Dym hierarchy and its supersymmetric extension
Kai Tian, Ziemowit Popowicz, Q. P. Liu
For the Harry Dym hierarchy, a non-standard Lax formulation is deduced from that of Korteweg-de Vries (KdV) equation through a reciprocal transformation. By supersymmetrizing this…
The transformations between N=2 supersymmetric KdV and HD equations
Kai Tian, Q. P. Liu
The N=2 supercomformal transformations are employed to study supersymmetric integrable systems. It is proved that two known N=2 supersymmetric Harry Dym equations are transformed i…
Nonlinear Schrödinger Equation: Generalized Darboux Transformation and Rogue Wave Solutions
Boling Guo, Liming Ling, Q. P. Liu
In this paper, we construct a generalized Darboux transformation for nonlinear Schrödinger equation. The associated -fold Darboux transformation is given both in terms of a summ…
The Even and Odd Supersymmetric Hunter - Saxton and Liouville Equations
Q. P. Liu, Ziemowit Popowicz, Kai Tian
It is shown that two different supersymmetric extensions of the Harry Dym equation lead to two different negative hierarchies of the supersymmetric integrable equations. While the…
Supersymmetric Reciprocal Transformation and Its Applications
Q. P. Liu, Ziemowit Popowicz, Kai Tian
The supersymmetric analog of the reciprocal transformation is introduced. This is used to establish a transformation between one of the supersymmetric Harry Dym equations and the s…
Darboux transformation for two component derivative nonlinear Schrödinger equation
Liming Ling, Q. P. Liu
In this paper, we consider the two component derivative nonlinear Schrödinger equation and present a simple Darboux transformation for it. By iterating this Darboux transformation,…
Supersymmetric Two-Boson Equation: Bilinearization and Solutions
Q. P. Liu, Xiao-Xia Yang
A bilinear formulation for the supersymmetric two-boson equation is derived. As applications, some solutions are calculated for it. We also construct a bilinear Backlund transforma…
Darboux transformation for the modified Veselov-Novikov equation
Delong Yu, Q. P. Liu, Shikun Wang
A Darboux transformation is constructed for the modified Veselov-Novikov equation.
Decouple a coupled KdV system of Nutku and Oguz
Heng Chun Hu, Q. P. Liu
A coupled KdV system with a free parameter proposed by Nutku and Oguz is considered. It is shown that the system passes the WTC's Painlevé test for arbitrary value of the parameter…