Nonlinear dissipative and dispersive electrostatic structures in unmagnetized relativistic electron-ion plasma with warm ions and trapped electrons

In this paper, we have investigated electrostatic solitary and shock waves in an unmagnetized relativistic electron-ion (ei) plasma in the presence of warm ions and trapped electrons. In this regard, we have derived the trapped Korteweg-de Vries Burgers (TKdVB) equation using the small amplitude approximation method, which to the best of our knowledge has not been investigated in plasmas. Since the TKdVB equation involves fractional nonlinearity on account of trapped electrons, we have employed a smartly crafted extension of the tangent hyperbolic method and presented the solution of the TKdVB equation in this paper. The limiting cases of the TKdVB equation yield trapped Burgers (TB) and trapped Korteweg-de Vries (TKdV) equations. We have also presented the solutions of TB and TKdV equations. We have also explored how the plasma parameters affect the propagation characteristics of the nonlinear structures obtained for these modified nonlinear partial differential equations. We hope that the present work will open new vistas of research in the nonlinear plasma theory both in classical and quantum plasmas.