\(N\)-fold Darboux transformation and double-Wronskian-typed solitonic structures for a variable-coefficient modified Kortweg-de Vries equation
This paper considers a variable-coefficient modified Korteweg-de Vries equation which appears in certain situations in fluids and plasmas. An \(N\)-fold Darboux transformation of a variable-coefficient Ablowitz-Kaup-Newell-Segur spectral problem is constructed via a gauge transformation. The reduction of this \(N\)-fold Darboux transformation provides multisoliton solutions for this variable-coefficient modified Korteweg-de Vries equation in terms of the double Wronskian determinant. Two- and three-soliton solutions are investigated through graphical representations and three different types of solitonic interactions are discussed: head-on and overtaking collisions and parallel solitons. It is explained how nonlinear, dispersive and dissipative terms affect the velocities of the solitons whilst the amplitudes of the waves depend on the perturbation term.
variable-coefficient modified Korteweg-de Vries model
scientific article; zbMATH DE number 6104581
scientific article