69 citations · 112 across the 8 of their papers we have counts for
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Asymptotic behavior analysis of solutions to the Heisenberg ferromagnet equation with the Schwartz initial data
Xumeng Zhou, Xianguo Geng, Bo Xue
This work aims to investigate the long-time asymptotic behavior of solutions to the Cauchy problem for the Heisenberg ferromagnet equation with the Schwartz initial data. Utilizing…
Periodic and rational solutions of the reduced Maxwell-Bloch equations
Jiao Wei, Xin Wang, Xianguo Geng
We investigate the reduced Maxwell-Bloch (RMB) equations which describe the propagation of short optical pulses in dielectric materials with resonant non-degenerate transitions. Th…
Algebro-geometric Constructions to the Dym-type Hierarchy
Lihua Wu, Guoliang He, Xianguo Geng
Resorting to the characteristic polynomial of Lax matrix for the Dym-type hierarchy, we define a trigonal curve, on which appropriate vector-valued Baker-Akhiezer function and mero…
The discrete mKdV equation revisited: a Riemann-Hilbert approach
Junyi Zhu, Xianguo Geng, Yonghui Kuang
We study the plus and minus type discrete mKdV equation. Some different symmetry conditions associated with two Lax pairs are introduced to derive the matrix Riemann-Hilbert proble…
The AB equations and the -dressing method in semi-characteristic coordinates
Junyi Zhu, Xianguo Geng
The dressing method based on the matrix -problem is generalized to study the canonical form of AB equations. The soliton solutions for the AB equations are…
Backlund Transformations of Soliton Systems from Symmetry Constraints
Wen-Xiu Ma, Xianguo Geng
Binary symmetry constraints are applied to constructing Bäcklund transformations of soliton systems, both continuous and discrete. Construction of solutions to soliton systems is s…