Several new soliton-like structures have been obtained under the consideration of non trivial boundary condition for the difference value of density in the thermodynamic model of nerve pulses. The model is based on thermodynamic principles of zero transfer of energy to the media. We have studied these solutions for particular values in the parameter space, and obtained both bell soliton on the condensate and bubble like solutions as typical non-topological representative solutions. The solutions will propagate along the nerve with constant velocity. The analysis of the properties of the solutions provides us with available permitted velocities and the prediction of the constant density value of the background at long distances far from the excited zone in the nerve.