Abstract
The effect of an isotropic pressure on longitudinal nonlinear plasma waves is investigated. Two distinct types of solitary wave solutions are found, one similar to the nonlinear zero pressure wave and a new type which is best described as a solitary wave within a solitary wave. The order of magnitude of the width of the first type of wave and the outer part of the second is the geometric mean of the gyroradii of the ions and electrons when moving with the Alfvén speed. It is found that the isotropic pressure shortens the width of the first type of wave. Both cases of unequal and equal ion and electron temperatures are investigated for the two types of waves.