Beyond solitons: Deformed solitary solutions to the mathematical model of tumor–immune system interactions

Abstract

The concept of the deformed solitary solutions is introduced in this paper. It is demonstrated that deformed solitary solutions to nonlinear differential equations can exist even if those equations do not admit classical solitary solutions. The proposed technique for the derivation of deformed solitary solutions does yield not only the analytical closed-form structure of the solution, but also automatically derives the conditions for its existence in the space of system parameters. Analytical and computational techniques are used to derive and to illustrate deformed kink solitary solutions to the mathematical model for tumor–immune system interactions.