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The pressure effect on the small amplitude solitary waves in a complex superthermal plasma composed of electrons, ions and dust is discussed. The Korteweg-de-Vries (KdV) equation and its model solution are derived using standard reduction perturbation techniques. Pressure is shown to significantly affects the existing mode in a superthermal environment. The imperative role is played here by the spectral index κ and the dust charge that strongly affect the properties of the nonlinear structures. The results obtained are compared with those acquired by the homotopy perturbation method (HPM). We see a strong correlation in the small time limit with our analytical calculations and those obtained by the HPM technique.

The specific role of ion heat flux on the characteristics of the linear and nonlinear ion temperature gradient (ηi) driven mode in inhomogeneous electron-positron-ion plasma is presented. Inhomogeneity in density, temperature, and the magnetic field is considered. A modified linear dispersion relation is obtained, and its different limiting cases are when ηi 2/3, ωD(gradient in magnetic field) = 0 and β(density ratio of plasma species) = 1 are discussed. Furthermore, an expression for the anomalous transport coefficient of the present model is obtained. Nonlinear structure solutions in the form of solitons and shocks show that mode dynamics enhance in the presence of ion heat flux in electron-positron-ion plasma. The present study is essential in energy confinement devices such as tokamak because the heat flux observed experimentally in tokamak plasma is much higher than those described by collisions. Further, it could be helpful to understand the nonlinear electrostatic excitations in the interstellar medium.

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