A Two-component Generalization of the Camassa-Holm Equation and its Solutions
- Ming Chen, Si‐Qi Liu, You-jin Zhang
- Mathematics
- 14 January 2005
An explicit reciprocal transformation between a two-component generalization of the Camassa–Holm equation, called the 2-CH system, and the first negative flow of the AKNS hierarchy is established.…
Bihamiltonian Cohomologies and Integrable Hierarchies I: A Special Case
- Si‐Qi Liu, You-jin Zhang
- Mathematics
- 29 August 2012
We present some general results on properties of the bihamiltonian cohomologies associated to bihamiltonian structures of hydrodynamic type, and compute the third cohomology for the bihamiltonian…
On Hamiltonian perturbations of hyperbolic systems of conservation laws I: Quasi‐Triviality of bi‐Hamiltonian perturbations
- B. Dubrovin, Si‐Qi Liu, You-jin Zhang
- Mathematics
- 1 October 2004
We study the general structure of formal perturbative solutions to the Hamiltonian perturbations of spatially one‐dimensional systems of hyperbolic PDEs vt + [ϕ(v)]x = 0. Under certain genericity…
Deformations of semisimple bihamiltonian structures of hydrodynamic type
- Si‐Qi Liu, You-jin Zhang
- Mathematics
- 8 May 2004
BCFG Drinfeld–Sokolov hierarchies and FJRW-theory
- Si‐Qi Liu, Y. Ruan, You-jin Zhang
- Mathematics
- 27 December 2013
According to the ADE Witten conjecture, which is proved by Fan, Jarvis and Ruan, the total descendant potential of the FJRW invariants of an ADE singularity is a tau function of the corresponding…
On quasi-triviality and integrability of a class of scalar evolutionary PDEs
- Si‐Qi Liu, You-jin Zhang
- Mathematics
- 11 October 2005
Hodge–GUE Correspondence and the Discrete KdV Equation
- B. Dubrovin, Si‐Qi Liu, Di Yang, You-jin Zhang
- MathematicsCommunications in Mathematical Physics
- 7 December 2016
We prove the conjectural relationship recently proposed in Dubrovin and Yang (Commun Number Theory Phys 11:311–336, 2017) between certain special cubic Hodge integrals of the Gopakumar–Mariño–Vafa…
Frobenius Manifolds and Central Invariants for the Drinfeld - Sokolov Bihamiltonian Structures
- B. Dubrovin, Si‐Qi Liu, You-jin Zhang
- Mathematics
- 16 October 2007
Hodge integrals and tau-symmetric integrable hierarchies of Hamiltonian evolutionary PDEs
- B. Dubrovin, Si‐Qi Liu, Di Yang, You-jin Zhang
- Mathematics
- 16 September 2014
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