The Improved exp⁡-Φξ-Expansion Method and New Exact Solutions of Nonlinear Evolution Equations in Mathematical Physics - Guiying Chen; Xiangpeng Xin; Hanze Liu (Advances in Mathematical Physics)
The exp(-Φ(ξ))-expansion method is improved by presenting a new auxiliary ordinary differential equation for Φ(ξ). By using this method, new exact traveling wave solutions of two important nonlinear evolution equations, i.e., the ill-posed Boussinesq equation and the unstable nonlinear Schrödinger equation, are constructed. The obtained solutions contain Jacobi elliptic function solutions which can be degenerated to the hyperbolic function solutions and the trigonometric function solutions. The present method is very concise and effective and can be applied to other types of nonlinear evolution equations.