Coupled KdV equations derived from atmospherical dynamics

Details Coupled KdV equations derived from atmospherical dynamics Coupled KdV equations derived from atmospherical dynamics

2005-08-22

arxiv.org/abs/nlin/0508029v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

19 pages, 2 figures

Scientific paper

10.1088/0305-4470/39/3/005

Some types of coupled Korteweg de-Vries (KdV) equations are derived from an atmospheric dynamical system. In the derivation procedure, an unreasonable $y$-average trick (which is usually adopted in literature) is removed. The derived models are classified via Painlev\'e test. Three types of $\tau$-function solutions and multiple soliton solutions of the models are explicitly given by means of the exact solutions of the usual KdV equation. It is also interesting that for a non-Painlev\'e integrable coupled KdV system there may be multiple soliton solutions.

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