Analysis of the dynamical properties for the cancer cells density inside a two dimensional growth spatial region

In this study, we will analyze the soliton dynamical behavior for a two-dimensional model depicting the density of cancer cells for the growth of human tumor tissue. We will consider two methods for this analysis: the modified Jacobi elliptic function method and the [Formula: see text] method. These methods will incorporate the net growth or decay of the cells due to outside control mechanisms, such as the effect of radiation therapy. We will construct solitons’ analytical expressions by using the sub-equation method with elliptical functions and the associated solutions of the [Formula: see text] method. By considering the arising constraints, we will determine a new entire family of solitons in a specific way over the parameter governing the external control growth. We will illustrate the analytical properties for the time evolution of the solitons in three-dimensional (3D) and two-dimensional (2D) plots. The mathematical functions used in this study have some attractive time evolution with a significant dependency on the elliptical parameters and [Formula: see text] coefficients. The solitons we report concerning tumor cell density in tumor proliferation will be valuable for future research endeavors involving the introduction of additional interactions.