The Soliton-Like Solutions of ϕ⁶ and ϕ⁴ + ϕ³ Models with and Without Dissipation¹

Besides the ϕ⁴ theory, the ϕ⁶ model and the ϕ⁴ + ϕ³ model are also useful in physics. Some specific types of solutions of them can be obtained from the solutions of ϕ⁴ model. The important solutions previously known are the special examples of ours. The dissipation equations of these models are also studied. The results indicate that the friction effects spread the singular solutions with velocity v = 1 (Heaviside function) of the undamped equations such that they are nonsingular and their velocities are lower than one.