Exact solutions of a nonlinear dispersive-dissipative equation. (English) Zbl 0896.35107
Summary: Within the invariant formalism of the Painlevé analysis, we derive new exact solutions of a nonlinear dispersive-dissipative equation, which describes weak nonlinear ion-acoustic waves in a plasma consisting of cold ions and warm electrons, in terms of Bessel functions. Furthermore, a travelling wave solution is also obtained in a particular case.
MSC:
35Q35 | PDEs in connection with fluid mechanics |
76X05 | Ionized gas flow in electromagnetic fields; plasmic flow |
35C05 | Solutions to PDEs in closed form |