Abstract:
The discrete analog of the periodic variant of the inverse scattering technique is used to construct exact periodic solutions of the discrete modified nonlinear Korteweg–de Vries equation.
Citation:
N. N. Bogolyubov (Jr.), A. K. Prikarpatskii, V. G. Samoilenko, “Discrete periodic problem for the modified nonlinear Korteweg–de Vries equation”, TMF, 50:1 (1982), 118–126; Theoret. and Math. Phys., 50:1 (1982), 75–81
This publication is cited in the following 8 articles:
Dong Gong, Xianguo Geng, “Algebro-geometric Constructions of Quasi Periodic Flows of the Discrete Self-dual Network Hierarchy and Applications”, JNMP, 22:3 (2021), 395
Babadjanova A., Kriecherbauer T., Urazboev G., “The Periodic Solutions of the Discrete Modified Kdv Equation With a Self-Consistent Source”, Appl. Math. Comput., 376 (2020), 125136
X. Zeng, X. Geng, “Quasiperiodic solutions of the discrete Chen–Lee–Liu hierarchy”, Theoret. and Math. Phys., 179:3 (2014), 649–678
Xin Zeng, Xianguo Geng, “Algebro-geometric solutions of the discrete Ragnisco-Tu hierarchy”, Reports on Mathematical Physics, 73:1 (2014), 17
Dong Gong, Xianguo Geng, “Explicit solutions for a hierarchy of differential–difference equations”, Applied Mathematics and Computation, 247 (2014), 898
XIANGUO GENG, DONG GONG, “QUASI-PERIODIC SOLUTIONS OF THE DISCRETE mKdV HIERARCHY”, Int. J. Geom. Methods Mod. Phys., 10:03 (2013), 1250094
Pritula, GM, “Stationary structures in two-dimensional continuous Heisenberg ferromagnetic spin system”, Journal of Nonlinear Mathematical Physics, 10:3 (2003), 256
V E Vekslerchik, “Finite-genus solutions for the Ablowitz-Ladik hierarchy”, J. Phys. A: Math. Gen., 32:26 (1999), 4983
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