Exact Explode-Decay Mode Solitary Wave Solution of the Classical Boussinesq Equation

抄録

Exact explode-decay mode solitary wave solutions of the one-dimensional classical Boussinesq and Burgers’ equations are obtained through the similarity variables. These solutions are expressed by the Gauss error functions, and have no divergent backgrounds. Also, it is shown that the two equations can be reduced to the Kummer, Whittaker’s, modified Bessel’s, Hermite’s, or Weber’s equation.