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In the presence of an applied uniform magnetic field B0, the properties of 2-dimensional (2D) magnetosonic solitary waves of relativistic amplitude in the plasma containing electron, light ions He+, and heavy ions O+ are presented. In the weakly relativistic limit, a Kadomtsev–Petviashvili (KP) equation is derived by reductive perturbation method. We give the N-soliton solution of the KP equation and find dromion solutions of a potential of the physical field. The interaction law of the dromions is obtained, which shows there is no exchange of energy, momentum, and angular momentum before and after interaction of the dromions except for phase shifts.

Two-dimensional (2D) relativistic magnetosonic solitons in the negative-ion-rich plasma consisting of positive ions Ar+, negative ions SF6- and electrons are investigated in the presence of an applied magnetic field B0 and can be described by a Kadomtsev–Petviashvili (KP) equation in the weakly relativistic limit. The ratio of positive ion density to negative ion density has a marked influence on the amplitudeΦm and width W of the steady-state KP soliton. The interaction law of the nontrivial solitons with rich web structure is studied by the Wronskian determinant method.

Considering the limiting weak nonlinearity, we obtained the solution of the coupled equations describing the interaction of ultraintense laser with cold transparent multicomponent plasma. It was indicated that the ions tend to accumulate at the center of the soliton and have large velocity when we consider the mobile ions in the multicomponent plasma, which shows that the result is different from that of the Berezhiani's analysis. The change of proportion of ions in the plasma has effects on the amplitude of vector potential and the maximum velocity of the soliton.

In the presence of an applied static and uniform magnetic field, a cylindrical Kadomtsev–Petviashivili equation is derived for a relativistic electromagnetic solitary wave propagating in collisionless plasma consisting electrons, positrons, and ions in the case of weak relativistic limit. This equation is solved in a stationary frame to obtain explicit expression for the velocity, amplitude and width of solitons. The amplitude of the solitary wave has a maximum value at a critical αc of the ratio of the ion equilibrium density to the electron one, and it increases as the applied magnetic field becomes larger.

The damage model and the rate equation of quartz glass were set up under charged particles irradiation, and the concentration of ions and electrons produced by ionization were also given. The mathematical fitted results of the change in optical density are in accordance with the experimental results. The model was also applied to optical Al film reflector, and the mathematical fitted results of the integral reflectance of Al film reflector were given. The proposed damage model can be used to describe quantitatively the change in optical property of quartz glass with increasing absorption dose under charged particles irradiation.