Complexiton Solutions of Nonlinear Partial Differential Equations Using a New Auxiliary Equation
Xue Liu *
School of Science, Linyi University, Linyi 276005, P. R. China and School of Mathematics Science, Shandong Normal University, Jinan 250014, P. R. China.
Huai-tang Chen *
School of Science, Linyi University, Linyi 276005, P. R. China and School of Mathematics Science, Shandong Normal University, Jinan 250014, P. R. China.
Shu-huan Yang
School of Science, Linyi University, Linyi 276005, P. R. China and School of Mathematics Science, Shandong Normal University, Jinan 250014, P. R. China.
*Author to whom correspondence should be addressed.
Abstract
In this paper, a novel auxiliary equation: φ′′ = a + bφ + cφ3 which has mutiple function solutions including trigonometric function, hyperbolic function and other functions, is considered. It is applied to a series of partial differential equations easily and effectively. It helps physicists to obtain complexiton solutions of nonlinear partial equations and analyze special phenomena accurately in their fields.
Keywords: Complexiton solution, Riccati equation, Partial differential equation