The hierarchy of the sine-Gordon equation with self-consistent sources is derived by using the eigenfunctions of recursion operator. The bilinear form of the sine-Gordon equation with self-consistent sources is given and the N-soliton solutions are obtained through Hirota method and Wronskian...

The bilinear form of the non-isospectral mKdV equation is given and the exact N-soliton solutions are obtained through Hirota method and Wronskian technique, respectively.

The Kadomtsev–Petviashvili (KP) equation describes weakly dispersive and small amplitude waves propagating in a quasi-two-dimensional situation. Recently a large variety of exact soliton solutions of the KP equation has been found and classified. Those soliton solutions are localized along...

In this paper, we would give a broad set of sufficient conditions of systems of linear partial differential equations which guarantee that the Grammian determinant solves the KP (Kadomtsev–Petviashvili) equation in the bilinear form. A systematic analysis of linear partial differential...

In this paper, we propose a new approach in the study of the dynamics of solitary waves over an erodible surface consisting of non-cohesive particles transported by a constant unidirectional fluid. Using the multiple scale perturbation method, we show that the system can be described by the...