Darboux transformation and soliton solutions for a variable-coefficient modified Kortweg-de Vries model from fluid mechanics, ocean dynamics, and plasma mechanics

This paper is to investigate a variable-coefficient modified Kortweg-de Vries (vc-mKdV) model, which describes some situations from fluid mechanics, ocean dynamics, and plasma mechanics. By the Ablowitz-Kaup-Newell-Segur procedure and symbolic computation, the Lax pair of the vc-MKdV model is derived. Then, based on the aforementioned Lax pair, the Darboux transformation is constructed and a new one-soliton-like solution is obtained as well. Features of the one-soliton-like solution are analyzed and graphically discussed to illustrate the influence of the variable coefficients in the solitonlike propagation.