N-soliton solutions to a -dimensional integrable equation

Extensions of Soliton equations to non-commutative (2 + 1) dimensions

“…NC KdV (2.13) (x, t) ¹ NC KP (3.7) (x, y, t) (3.2) (z) On commutative case, it is known that (2+1) dimensional integrable equations is given by combinating the extension (3.1) with the extension (3.2) [13,14,15]. We would like to study here the combination on NC case.…”

“…In the commutative limit, equation (3.24) reads the extended BCS equation, which has soliton solutions [13]. So we refer to equation (3.24) as the NC extended BCS equation.…”

The Investigation into New Equations in (2 + 1) Dimensions

“…For that, we modify the above T operator to include another spatial dimension(z) [4,5,6,7,8] as follows,…”

Lax Pairs, Painlevé Properties and Exact Solutions of the Calogero Korteweg-de Vries Equation and a New (2 + 1)-Dimensional Equation

“…In [7,8,9], we developed the construction method for higher-dimensional integrable equation. For example, we considered the Calogero-Bogoyavlenskij-Schiff (CBS) equation [10,11,12,13,14,15,16], 14) and the modified Calogero-Bogoyavlenskij-Schiff (mCBS) [15],…”

“…The above integral factor is rewritten as 8) where 10) that is, f N −1 is of the same structure as f N , except for the j index. Equation (4.8) is differentiated with respect to x, i.e.,…”