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Abstract: The generalized nonlinear and equations with variable coefficients are investigated under suitable conditions. Applying the auxiliary differential equation techniques, we derive various explicit travelling wave solutions with different physical structures for the equations. It is shown that the solutions include several existing solutions and the variable coefficients of the derivative terms of the equations determine the physical structures of the solutions. [Copyright &y& Elsevier]

Abstract: Mathematical techniques based on an auxiliary equation and the symbolic computation system Matlab are employed to investigate a generalized Benjamin–Bona–Mahony partial differential equation. The Jacobi elliptic function solutions, the degenerated soliton solutions and the triangle function solutions to the equation are obtained under certain circumstances. [Copyright &y& Elsevier]

Abstract: A mathematical technique based on an auxiliary equation and the symbolic computation system Matlab is developed to construct the exact solutions for a generalized Camassa–Holm equation and a nonlinear dispersive equation with variable coefficients. It is shown that the variable coefficients of the derivative terms in the equations cause the qualitative change in the physical structures of the solutions. [Copyright &y& Elsevier]