TY - JOUR AU - Ruggieri, Marianna AU - Speciale, Maria Paola PY - 2013 DA - 2013/12/05 TI - Similarity reduction and closed form solutions for a model derived from two-layer fluids JO - Advances in Difference Equations SP - 355 VL - 2013 IS - 1 AB - In this paper, we study an integrable system of coupled KdV equations, derived by Gear and Grimshaw (Stud. Appl. Math. 70(3):235-258, 1984), modeling the strong interaction of two-dimensional, long, internal gravity waves propagating on neighboring pycnoclines in a stratified fluid. In particular, we present the complete group classification of the model and find conditions on arbitrary parameters for which the system admits symmetries. Some exact solutions of physical relevance are derived. SN - 1687-1847 UR - https://doi.org/10.1186/1687-1847-2013-355 DO - 10.1186/1687-1847-2013-355 ID - Ruggieri2013 ER -