The homotopy analysis method is applied to solve the variable coefficient KdV-Burgers equation. With the aid of generalized elliptic method and Fourier’s transform method, the approximate solutions of double periodic form are obtained. These solutions may be degenerated into the approximate solutions of hyperbolic function form and the approximate solutions of trigonometric function form in the limit cases. The results indicate that this method is efficient for the nonlinear models with the dissipative terms and variable coefficients.
Dianchen Lu. Jie Liu. "Application of the Homotopy Analysis Method for Solving the Variable Coefficient KdV-Burgers Equation." Abstr. Appl. Anal. 2014 (SI21) 1 - 4, 2014. https://doi.org/10.1155/2014/309420