The gauge transformation of the q-deformed modified KP hierarchy

References

• M. Adler, On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-devries type equations, Invent. Math. 50 (1979) 219–248.
   Web of Science ®Google Scholar
• M. Adler, E. Horozov and P. van Moerbeke, The solution to the q-KdV equation, Phys. Lett. A 242 (1998) 139–151.
   Web of Science ®Google Scholar
• H. Aratyn, E. Nissimov and S. Pacheva, Darboux-Backlund solutions of SL(p,q) KP-KdV hierarchies, constrained generalized Toda lattices, and two-matrix string model, Phys. Lett. A 201 (1995) 293–305.
   Web of Science ®Google Scholar
• L. L. Chau, J. C. Shaw and M. H. Tu, Solving the constrained KP hierarchy by gauge transformations, J. Math. Phys. 38 (1997) 4128–4137.
   Web of Science ®Google Scholar
• L. L. Chau, J. C. Shaw and H. C. Yen, Solving the KP hierarchy by gauge transformations, Comm. Math. Phys. 149 (1992) 263–278.
   Web of Science ®Google Scholar
• J. P. Cheng and J. S. He, The applications of the gauge transformation for the BKP hierarchy, J. Math. Anal. Appl. 410 (2014) 989–1001.
   Web of Science ®Google Scholar
• E. Frenkel and N. Reshetikhin, Quantum affine algebras and deformations of the Virasoro and Walgebras, Comm. Math. Phys. 178 (1996) 237–264.
   Web of Science ®Google Scholar
• J. S. He, Y. Cheng and R. A. Roemer, Solving bi-directional soliton equations in the KP hierarchy by gauge transformation, J. High Energy Phys. 03 (2006) 103.
   Google Scholar
• J. S. He, Y. H. Li and Y. Cheng, q-deformed KP hierarchy and q-Deformed constrained KP hierarchy, SIGMA 2 (2006) 060.
   Google Scholar
• J. S. He, Y. S. Li and Y. Cheng, Two choices of the gauge transformation for the AKNS hierarchy through the constrained KP hierarchy, J. Math. Phys. 44 (2003) 3928–3960.
   Web of Science ®Google Scholar
• J. S. He, Z. W. Wu and Y. Cheng, Gauge transformations for the constrained CKP and BKP hierarchies, J. Math. Phys. 48 (2007) 113519.
   Web of Science ®Google Scholar
• P. Iliev, Tau function solutions to a q-deformation of the KP hierarchy, Lett. Math. Phys. 44 (1998) 187–200.
   Web of Science ®Google Scholar
• A. Klimyk and K. Schmdgen, Quantum groups and their representations (Springer, Berlin, 1997).
   Google Scholar
• R. L. Lin, X. J. Liu and Y. B. Zeng, A new extended q-deformed KP hierarchy, J. Nonlin. Math. Phys. 15 (2008) 333–347.
   Web of Science ®Google Scholar
• R. L. Lin, H. Peng and M. Manas, The q-deformed mKP hierarchy with self-consistent sources, Wron-skian solutions and solitons, J. Phys. A: Math. Theor. 43 (2010) 434022.
   Web of Science ®Google Scholar
• S. W. Liu, Y. Cheng and J. S. He, The determinant representation of the gauge transformation for the discrete KP hierarchy, Sci. China Math. 53 (2010) 1195–1206.
   Web of Science ®Google Scholar
• S. Majid, Foundations of quantum group theory (Cambridge University Press, Cambridge, 1995).
   Google Scholar
• J. J. C. Nimmo, Darboux transformations from reductions of the KP hierarchy, Nonlinear Evolution Equations and Dynamical Systems, eds. V. G. Makhankov, A. R. Bishop, and D. D. Holm (World Scientific, Singapore, 1995) 168–177.
   Google Scholar
• W. Oevel, Darboux theorems and Wronskian formulas for integrable system I: constrained KP flows, Physica A 195 (1993) 533–576.
   Web of Science ®Google Scholar
• W. Oevel, Darboux transformations for integrable lattice systems, Nonlinear Physics: theory and experiment, eds. E. Alfinito, L. Martina and F. Pempinelli (World Scientific, Singapore, 1996) 233–240.
   Google Scholar
• W. Oevel and C. Rogers, Gauge transformations and reciprocal links in 2+1 dimensions, Rev. Math. Phys. 5 (1993) 299–330.
   Web of Science ®Google Scholar
• K. Takasaki, q-Analogue of modified KP hierarchy and its quasi-classical Limit, Lett. Math. Phys. 72 (2005) 165–181.
   Web of Science ®Google Scholar
• K. L. Tian, J. S. He, Y. C. Su and Y. Cheng, String equations of the q-KP hierarchy, Chin. Ann. Math. B. 32 (2011) 895–904.
   Web of Science ®Google Scholar
• K. L. Tian, J. S. He and Y. C. Su, Symmetric q-deformed KP hierarchy, arXiv:1403.0169.
   Google Scholar
• M. H. Tu, J. C. Shaw and C. R. Lee, On Darboux-Backlund transformations for the q-deformed Korteweg-de Vries hierarchy, Lett. Math. Phys. 49 (1999) 33–45.
   Web of Science ®Google Scholar
• M. H. Tu, J. C. Shaw and C. R. Lee, On the q-deformed modified Korteweg-de Vries hierarchy, Phys. Lett. A 266 (2000) 155–159.
   Web of Science ®Google Scholar
• S. K. Wang, K. Wu, X. N. Wu and D. L. Yu, The q-deformation of AKNS-D hierarchy, J. Phys. A: Math. Gen. 34 (2001) 9641–9651.
   Google Scholar
• R. Willox, I. Loris and C. R. Gilson, Binary Darboux transformations for constrained KP hierarchies, Inverse Problems 13 (1997) 849–865.
   Web of Science ®Google Scholar