Xia, Tiecheng; Zhang, Hongqing; Yan, Zhenya New explicit and exact travelling wave solutions for a class of nonlinear evolution equations. (English) Zbl 0982.35101 Appl. Math. Mech., Engl. Ed. 22, No. 7, 788-793 (2001). Summary: With the help of Mathematica, many solutions for a class of nonlinear evolution equations \[ u_{tt}+ au_{xx}+ bu+ cu^2+ du^3= 0 \] are obtained by using the hyperbola function method and the Wu elimation methods, which include new travelling wave solutions, periodic solutions and kink soliton solutions. Some equations such as Duffing equation, sine-Gordon equation, \(\phi^4\) and Klein-Gordon equation are particular cases of the evolution equations. The method can also be applied to other nonlinear equations. Cited in 4 Documents MSC: 35Q53 KdV equations (Korteweg-de Vries equations) 35-04 Software, source code, etc. for problems pertaining to partial differential equations 35C05 Solutions to PDEs in closed form Keywords:travelling wave solutions; periodic solutions; kink soliton solutions; Duffing equation; sine-Gordon equation; Klein-Gordon equation Software:Mathematica PDFBibTeX XMLCite \textit{T. Xia} et al., Appl. Math. Mech., Engl. Ed. 22, No. 7, 788--793 (2001; Zbl 0982.35101) Full Text: DOI