Coupled Langmuir and ion-acoustic waves in two-electron temperature plasmas

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Abstract
The nonlinear propagation of coupled Langmuir and ion-acoustic waves in a two-electron temperature plasma is shown to be governed by a generalized Schrödinger–Boussinesq system, which for uni-directional propagation reduces to the coupled Schrödinger–Korteweg-de Vries (K-dV) system. For stationary propagation of the coupled waves, the Schrödinger–Boussinesq (or K-dV) system leads to a generic Hamiltonian which is shown to be integrable in the sub- as well as supersonic regimes of the Mach number. Different classes of exact analytical solutions of the stationary Schrödinger–Boussinesq system are explicitly obtained. Two-electron temperature plasmas are shown to admit a new class of coupled Langmuir–ion-acoustic solitons which propagate with supersonic speeds but are accompanied by density rarefactions. We also derive exact governing equations valid for large amplitude waves, and obtain their approximate solutions. Existence conditions for large amplitude localized solutions in the quasi-neutral limit are derived. A comparison between different types of governing equations and their analytical solutions is carried out.