Soliton solutions for (2+1)-dimensional and (3+1)-dimensional K(m, n) equations

We consider the nonlinear dispersive K(m, n) equation with the generalized evolution term and derive analytical expressions for some conserved quantities. By using a solitary wave ansatz in the form of sech(p) function, we obtain exact bright soliton solutions for (2 + 1)-dimensional and (3 + 1)-dimensional K(m, n) equations with the generalized evolution terms. The results are then generalized to multi-dimensional K(m, n) equations in the presence of the generalized evolution term. An extended form of the K(m, n) equation with perturbation term is investigated. Exact bright soliton solution for the proposed K(m, n) equation having higher-order nonlinear term is determined. The physical parameters in the soliton solutions are obtained as function of the dependent model coefficients. (C) 2009 Elsevier Inc. All rights reserved.