Soliton-like solution of the modified korteweg- DE vries equation

Summary form only given. It is known that propagation of non-linear dust ion acoustic wave (small amplitude) can be described by modified Korteweg-de Vries-Burgers (mKdVB) equation. The paper is relevant to the study of ion-acoustic solitary waves in the double plasma device. The dissipation of solitary waves in the presence of dusty particles are compared numerically mKdVB in this work. The Landau damping effect in dissipation was negligible according to the high ratio of electron/ion temperature and long wave approximation. Some experimental and theoretical arguments for existence of new type of dissipation in dusty plasma were getting earlier. Usual processes: ion-dust collisions and ion kinematic viscosity were involved in analysis too. But values of plasma parameters into experimental device are corresponding to the weak collision plasma. So we can neglect the ion kinematic viscosity in a first approximation. The mKdVB equation is transformed to mKdV in this case. It is interesting that we can re-arrange last equation into cylindrical KdV (cKdV) by special kind of transformations. Namely this type of equation (cKdV) was used in the investigation of cylindrical ion acoustic soliton propagation into collisionless plasma. In general case the cKdV is integrable by the inverse transforms and the Backlund transformation has been found. Some exact solutions for cKdV are complicated combination of Airy functions. The main features of cKdV solution may be received according to the method. The full set of the experimental data are matched with the regularities from cKdV solution