Traveling wave solutions for some factorized nonlinear PDEs

Abstract

In this work, some new special traveling wave solutions of the convective Fisher equation, the time-delayed Burgers–Fisher equation, the Burgers–Fisher equation and a nonlinear dispersive–dissipative equation (Kakutani and Kawahara 1970 J. Phys. Soc. Japan 29 1068) are obtained through the factorization technique. All of them share the same type of factorization scheme, which reduces the original equation to a Riccati equation of the same kind, whose general solution is given in terms of Bessel and Neumann functions. In addition, some novel particular solutions of the nonlinear dispersive–dissipative equation are provided.