No abstract

The stability of the solitary-wave solutions of the nonlinear cubic–quintic Schrödinger equation (NLCQSE) is examined numerically. The solutions are found not to be solitons, but quasi-soliton behaviour is found to persist over wide regions of parameter space. Outside these regions dispersive and explosive behaviour is observed in solitary-wave interactions.

The electric currents in living tissues have interested physiologists ever since their existence was proved by Du Bois Reymond, but little was done towards explaining their origin and magnitude on a quantitative physico-chemical basis befor the pioneer researches og J. S. Macdonald. Work previous to Macdonald's has discussed fully by that anuthor (1902), hence it will not be mentioned here. macdonald found that the injury potential of medullated nerve, either frog's or mammal's (1900, a, b ; 1902), could be given a value greater or smaller than the normal by simply altering the concentration of the solution in contact with the external surfaces of the fibres. He showed that solutions of NaOH, HCl, NaCl, or KCl affected the potential according to their concentrations and that the relationship between the two variables was a logarithmic one, which fact was in agreement with the then new theory of concentration cells developed by Nernst. Macdonald went on to point out (1902) that the effects of potassium chloride solutions were particularly interesting, and to suggest that the difference between the concentration of potassium in the axis cylinder of the nerve and in the surrounding blood or salt solution was wholly responsible for the observed injury potential. Over a wide range of concentration, 1/8 to 1 molar, he demonstrated that there was nearly a linear relation between the injury potential and the logarithm of the potassium ion concentration. However, since he simply varied the concentrations of his electrolyte solutions, and made no effort to maintain them isotonic with blood by the addition of a non-electrolyte, exception might be taken to some of his results on the ground that the effects were due in part to the passage of water into or out of the nerve with a consequent dilution or concentration of the plasma.