Soliton Solution to Extended Volterra Equation

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“…In the case where V n are scalars, we write a n instead of V n and the last two equations turn out to be the "extended Lotka-Volterra equations" studied in [3,6]. For q = 1, they reduce toȧ n = a n (a n+1 · · · a n+p−1 −a n−p+1 · · · a n−1 ) andȧ n = a…”

“…It may be regarded as a special case of a parameter-dependent zero curvature condition. In this work we derive generalized Lotka-Volterra (LV) lattices (see [3,4,5,6,7], for example) from a "master equation" with a bicomplex formulation. Some consequences of the latter (conservation laws [1], Bäcklund transformations [2]) are briefly discussed.…”

Reductions of integrable lattices

“…There are different methods for constructing integrable lattices and its explicit solutions, such that Lax pairs, recursion operators etc. For consulting, see, for example, [1], [2], [3], [5], [6], [10], [11], [13], [18]. In Refs.…”

Solutions for a System of Difference-Differential Equations Related to the Self-Dual Network Equation

“…i) The extended Volterra equation. 20) ii) The Volterra equation of the Hirota-Satsuma type. 1) iii) A system of complex discrete KdV equations.…”