A method for solving model nonlinear equations describing plasma oscillations in the presence of viscosity and resistivity is given. By first going to the Lagrangian variables and then transforming the space variable conveniently, the solution in parametric form is obtained. It involves simple elementary functions. Our solution includes all known exact solutions for an ideal cold plasma and a large class of new ones for a more realistic plasma. A new nonlinear effect is found of splitting of the largest density maximum, with a saddle point between the peaks so obtained. The method may sometimes be useful where inverse scattering fails.

• Received 4 September 2008

DOI:https://doi.org/10.1103/PhysRevLett.102.145005