Exact solutions of nonlinear dispersive K(m, n) model with variable coefficients

The variable-coefficient Korteweg-de Vries (KdV) equation with additional terms contributed from the inhomogeneity in the axial direction and the strong transverse confinement of the condense was presented to describe the dynamics of nonlinear excitations in trapped quasi-one-dimensional Bose–Einstein condensates with repulsive atom–atom interactions. To understand the role of nonlinear dispersion in this variable-coefficient model, we introduce and study a new variable-coefficient KdV with nonlinear dispersion (called vc-K(m, n) equation). With the aid of symbolic computation, we obtain its compacton-like solutions and solitary pattern-like solutions. Moreover, we also present some conservation laws for both vc-K+(n, n) equation and vc-K−(n, n) equation.