Analytical solution of variant Boussinesq equations

Abstract

In this paper, analytic solutions of the variant Boussinesq equations are obtained by the homotopy analysis and the homotopy Padé methods. The obtained approximation using homotopy method contains an auxiliary parameter, which is a simple way to control and adjust the convergence region and rate of solution series. The approximation solutions by [m,m] homotopy Padé technique is often independent of auxiliary parameter ℏ, and this technique accelerates the convergence of the related series. Copyright © 2013 John Wiley & Sons, Ltd.

Application of Tanh Method to Complex Coupled Nonlinear Evolution Equations

“…Therefore the solutions in [26] and [27] turn out to be special cases of the results from this paper. Later, this paper will be studied further along.…”

“…Compared with the existing methods [26,27], our method further exceeds their applicability in obtaining a series of exact travelling wave solutions. In this section, we compare with some existing results:…”

“…• The solution (21) with positive sign are equivalent to the solutions (4.21) and (48) in [26] and [27], respectively.…”

“…The (2 + 1)-dimensional nonlinear complex coupled Maccari equations are the second complex coupled equations that will be discussed i u t + u xx + uv = 0, v t + v y + (|u| 2 ) x = 0, (40) using the transformations • The solution (46) with positive sign are equivalent to the solutions (5.21) and (61) in [26] and [27], respectively.…”

“…The complex coupled Maccari equations is a nonlinear evolution equations described the motion of the isolated waves, localized in a small part of space, in many fields such as hydrodynamic, plasma physics, nonlinear optics and others [22][23][24][25][26][27][28]. Complex coupled Maccari equation derived from the Kadomtsev-Petviashvili equation (the best known two-dimensional generalizations of the KdV equation) and can be written in the form i u t + u xx + uv = 0,…”