Electrostatic nonlinear waves which transfer energy through the semiconductor are investi-
gated. A quantum hydrodynamic plasma system composed of self-streaming electrons and holes
is examined. The basic equations are reduced to one evolution equation called a modified nonlin-
ear Schr ̈odinger (mNLS) equation. The stability and instability regions are studied with respect
to the wavenumber and different plasma effects such as degenerate pressure, Bohm potential, and
collisions. The mNLS equation is solved analytically to obtain three kinds of nonlinear envelope
wave packet modes. It is found that there are different regions of stability and instability depend-
ing on various quantum effects. The electrons’ and holes’ self-streaming velocity is studied and
manipulated for the three types of nonlinear envelope waves ”dark soliton, bright soliton, and
rogue wave”. The dark envelope wave packet is generated in a stable region. When the electrons
and holes streaming velocities become faster, the wave amplitude becomes taller and the pulses
have higher frequency. The bright envelope wave packet exists in the unstable region. For low
streaming velocities, the rogue wave amplitude becomes shorter, however, when the streaming
velocities reach a critical value the amplitude increases suddenly six times. The self-heating could
be produced as the tunneling electrons and holes exchange their energy with the lattice, which
may decrease the lifetime of the semiconductors. The present results are helpful in realizing the
physical solution to the intrinsic heating problem in semiconductors.

Electron–hole pairs in semiconductors can be stimulated by a laser beam with energy larger than the energy gap of the semiconductor. The interaction between an electron–hole plasma with a laser beam can be a source of instability. The dependence of the instability on the electron and hole temperatures and the unperturbed potential of the incident laser are examined. Using Maxwell’s equations along with electron–hole fluid equations, an evolution equation describing the system is obtained. The latter is reduced to an energy equation that characterizes localized pulse propagation.

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We follow theoretically the motion of the sodium atoms in vapor state under the influence of a laser mode in (1 + 1) D, which is achieved by introducing different optical filters. In the Dirac interaction representation, the equations of motion are represented via the Bloch form together with the Pauli operators to find the elements of the density matrix of the system. The emergence of the principle of coherence in varying the angles of the laser mode permits the evaluation of the average force affecting the atoms' acceleration or deceleration, and hence the corresponding velocities and temperatures are investigated. The atomic vapor is introduced in a region occupied by a heat bath presented by the laser field, such that the state of the atomic vapor is unstable inside the system due to the loss or gain of its kinetic energy to or from the laser field. This instability is studied by finding the eigenvalues of the system's entropy. Resorting to the assumption of Botin, Kazantsev, and Pusep, who issued in the presence of the weak and strong spontaneous emission, a coupling between the mean numbers of photons in terms of time, which allows the evaluation of the rate of entropy production of the system under study. No singularities are found throughout the process of equations solving and other calculations. Resorting to symbolic software, a set of figures illustrating the nonlinear behavior in the dynamics of the problem is present. In this paper, we introduce a theoretical study of the effect of two-counter propagation traveling plane waves on the motion of the sodium atoms in the vapor state by varying the coherence angles to investigate the atomic behavior. Good agreements are found with previous studies.