Publications and Preprints



  1. Liu, Si-Qi; Yang, Di; Zhang, Youjin; Zhou, Chunhui. The loop equation for special cubic Hodge integrals. Preprint arXiv: 1811.10234. (arXiv)
  2. Liu, Si-Qi; Wu, Chao-Zhong; Zhang, Youjin Zhang; Zhou, Xu. Drinfeld-Sokolov hierarchies and diagram automorphisms of affine Kac-Moody algebras. Preprint arXiv: 1811.10137. (arXiv)
  3. Liu, Si-Qi; Zhang, Youjin; Zhou, Chunhui. Fractional Volterra hierarchy. Lett. Math. Phys. 108 (2018), 261--283. (arXiv) (Journal)
  4. Dubrovin, Boris; Liu, Si-Qi; Zhang, Youjin. Bihamiltonian cohomologies and integrable hierarchies II: the tau structures. Comm. Math. Phy. 361 (2018), 467--524. (arXiv) (Journal)
  5. Dubrovin, Boris; Liu, Si-Qi; Yang, Di; Zhang, Youjin. Hodge-GUE correspondence and the discrete KdV equation. Preprint arXiv: 1612.02333. (arXiv)
  6. Liu, Si-Qi; Zhang, Youjin; Zhou, Xu. Central invariants of the constrained KP hierarchies. J. Geom. Phys. 97 (2015), 177--189. (arXiv) (Journal)
  7. Dubrovin, Boris; Liu, Si-Qi; Yang, Di; Zhang, Youjin. Hodge integrals and tau-symmetric integrable hierarchies of Hamiltonian evolutionary PDEs. Adv. Math. 293 (2016), 382--435. (arXiv) (Journal)
  8. Liu, Si-Qi; Ruan, Yongbin; Zhang, Youjin. BCFG Drinfeld-Sokolov hierarchies and FJRW-theory. Invent. Math. 201 (2015), 711--772. (arXiv) (Journal)
  9. Liu, Si-Qi; Yang, Di; Zhang, Youjin. Uniqueness theorem of $\mathcal{W}$-constraints for simple singularities. Lett. Math. Phys. 103 (2013), 1329--1345. (arXiv) (Journal)
  10. Fu, Yulong; Liu, Si-Qi; Zhang, Youjin; Zhou, Chunhui. Proof of a conjecture on the genus two free energy associated to the $A_n$ singularity. J. Geom. Phys. 76 (2014), 10--24. (arXiv) (Journal)
  11. Liu, Si-Qi; Zhang, Youjin. Bihamiltonian cohomologies and integrable hierarchies I: a special case. Comm. Math. Phy. 324 (2013), 897--935. (arXiv) (Journal)
  12. Dubrovin, Boris; Liu, Si-Qi; Zhang, Youjin. On the genus two free energies for semisimple Frobenius manifolds. Russ. J. Math. Phys. 19 (2012), 273--298. (arXiv) (Journal)
  13. Liu, Si-Qi; Xu, Dingdian; Zhang, Youjin. The inversion symmetry of the WDVV equations and tau functions. Phys. D 241 (2012), 2168--2177. (arXiv) (Journal)
  14. Liu, Si-Qi; Wu, Chao-Zhong; Zhang, Youjin. On the Drinfeld-Sokolov hierarchies of $D$ type. Int. Math. Res. Not. IMRN 2011, 1952--1996. (arXiv) (Journal)
  15. Liu, Si-Qi; Zhang, Youjin. Jacobi structures of evolutionary partial differential equations. Adv. Math. 227 (2011), 73--130. (arXiv) (Journal)
  16. Chen, Ming; Liu, Si-Qi; Zhang, Youjin. Hamiltonian structures and their reciprocal transformations for the $r$-KdV-CH hierarchy. J. Geom. Phys. 59 (2009), 1227--1243. (arXiv) (Journal)
  17. Liu, Si-Qi; Wu, Chao-Zhong; Zhang, Youjin. On properties of Hamiltonian structures for a class of evolutionary PDEs. Lett. Math. Phys. 84 (2008), 47--63. (arXiv) (Journal)
  18. Dubrovin, Boris; Liu, Si-Qi; Zhang, Youjin. Frobenius manifolds and central invariants for the Drinfeld-Sokolov bihamiltonian structures. Adv. Math. 219 (2008), 780--837. (arXiv) (Journal)
  19. Liu, Si-Qi; Zhang, Youjin. On quasi-triviality and integrability of a class of scalar evolutionary PDEs. J. Geom. Phys. 57 (2006), 101--119. (arXiv) (Journal)
  20. Chen, Ming; Liu, Si-Qi; Zhang, Youjin. A two-component generalization of the Camassa-Holm equation and its solutions. Lett. Math. Phys. 75 (2006), 1--15. (arXiv) (Journal)
  21. Dubrovin, Boris; Liu, Si-Qi; Zhang, Youjin. On Hamiltonian perturbations of hyperbolic systems of conservation laws. I. Quasi-triviality of bi-Hamiltonian perturbations. Comm. Pure Appl. Math. 59 (2006), 559--615. (arXiv) (Journal)
  22. Liu, Si-Qi; Zhang, Youjin. On the quasitriviality of deformations of bihamiltonian structures of hydrodynamic type. Preprint arXiv: math/0406626. (arXiv)
  23. Liu, Si-Qi; Zhang, Youjin. Deformations of semisimple bihamiltonian structures of hydrodynamic type. J. Geom. Phys. 54 (2005), 427--453. (arXiv) (Journal)