The physical structures of solutions for generalized K(n,n)K(n,n) and BBMBBM equations with variable coefficients

The generalized nonlinear K(n,n)K(n,n) and BBMBBM 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.