Multiple soliton solutions and other solutions of a variable-coefficient Korteweg–de Vries equation

Abstract

In this paper, we construct multiple soliton solutions of a time-dependent variable-coefficient Korteweg–de Vries equation in the form of bright, dark and singular soliton solutions. Furthermore, the periodic solutions are derived. These will be achieved via the aid of solitary wave ansatz methods. In addition, other exact solutions of a time-dependent variable-coefficient Korteweg–de Vries equation are attained using symmetry reductions. In one special case, the power series method is employed to derive a solution of the aforesaid equation. We also examine the conservation laws of the aforementioned equation using the variational approach. A brief physical representation of the derived conserved vectors will be conversed.