Painlevé property, soliton-like solutions and complexitons for a coupled variable-coefficient modified Korteweg–de Vries system in a two-layer fluid model

Conservation Laws for a Degasperis Procesi Equation and a Coupled Variable-Coefficient Modified Korteweg-de Vries System in a Two-Layer Fluid Model via the Multiplier Approach

“…System (23) was proposed in [18] as an important particular case of the formidable generalized coupled variablecoefficient modified Korteweg-de Vries (CVmKdV) system. The (CVmKdV) system was derived by Gao and Tang [19] as a two-layer model describing atmospheric and oceanic phenomena like interactions between the atmosphere and ocean, atmospheric blocking, oceanic circulations, hurricanes, typhoons, and so forth.…”

Conservation laws for a coupled variable-coefficient modified Korteweg–de Vries system in a two-layer fluid model

“…In (2), r i e e i , i = 1, ..., 13, are arbitrary functions of t. In the work [2] Gao and Tang found several solutions of (2) under some constraints on its coefficients. In [1] Zhu et al obtained the system (1) by a reduction different than the constraints used in [2], expecting that it could describe more complex physical properties than those investigated in other works (see [1] and the references therein). In the same paper various wide classes of interesting exact solutions were found.…”

“…The system (1) was proposed in [1] as an important particular case of the formidable generalized coupled variable-coefficient modified Korteweg-de Vries (CVmKdV) system          u t + r 1 u xxx + (r 2 u 2 + r 3 uv + r 4 u + r 5 v 2 + r 6 v + r 7 )u x + (r 8 u 2 + r 9 uv + r 10 u + r 11 v + r 12 )v x + r 13 u = 0, v t + e 1 v xxx + (e 2 v 2 + e 3 uv + e 4 v + e 5 u 2 + e 6 u + e 7 )v x + (e 8 v 2 + e 9 uv + e 10 v + e 11 u + e 12 )u x + e 13 v = 0,…”