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\(N\)-soliton solution of a lattice equation related to the discrete MKdV equation. (English) Zbl 1226.37050

In the previous article [“Solutions for a system of difference-differential equations related to the self-dual network equation”, Prog. Theor. Phys. 106, No. 6, 1079–1096 (2001; Zbl 1017.37036)], the author proposed a system of lattice equations related to the self-dual network equation and presented its solutions. Here, for the modification of this system in the form
\[ \dot v_n=4(v_{n-1}+v_{n+1})v^2_n/(1+v_{n-1}v_n)(1+v_n v_{n+1}) \]
related to the discrete MKdV equation, with an arbitrary boundary value at infinity, an \(N\)-soliton solution is obtained.

MSC:

37L60 Lattice dynamics and infinite-dimensional dissipative dynamical systems
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)

Citations:

Zbl 1017.37036
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References:

[1] Narita, K., Solutions for a system of difference-differential equations related to the self-dual network equation, Progr. theoret. phys., 106, 1079-1096, (2001) · Zbl 1017.37036
[2] Hirota, R.; Satsuma, J., A variety of nonlinear network equations generated from the Bäcklund transformation for the Toda lattice, Progr. theoret. phys. suppl., 59, 64-100, (1976)
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