Singularities in the Boussinesq equation and in the generalized Korteweg-de Vries equation.
In this paper, two kinds of analytic singular solutions (finite-time and infinite-time singular solutions) of two classical wave equations (the Boussinesq equation and a generalized Korteweg-de Vries equation) are obtained by means of the improved homogeneous balance method and a nonlinear transformation. The solutions show that special singular wave patterns exist in the classical models of shallow water wave problem.
Lei
Y
Y
Department of Physics, Lanzhou University, Gansu 730000, China.
Kongqing
Y
Y