Lie symmetries, exact wave solutions and conservation laws of nonlinear Bogovalenskii Breaking-Soliton equation for Nerve pulse propagation

In this article, Lie point symmetries are used for carrying out the exact solitary wave solutions of the (2+1)- Bogovalenskii Breaking-Soliton equation. Using novel solitary wave solutions and their interactions, we hope to gain a better understanding of how dispersion influences pulse propagation in the neuroscience field. By applying the invariance property of Lie groups, the possible infinitesimal generators and infinite-dimensional algebra of symmetry are assembled. Then, similarity variables are employed for the reduction of the test problem and transformed into ordinary differential equations. These equations construct exact solutions under some parametric restrictions. Furthermore, the establishment of the conserved vectors, along with associated symmetries, is done under the Lagrangian formulation. To portray the dynamic characteristics of the presented solutions, putting different sets of values of the parameters elucidates these solutions through numerical simulations in 3-dimensional and contour plots. Consequently, various kinds of exact solutions, including breather solutions, rouge solutions, and lump solutions, as well as their elastic description, are systematically discussed in order to validate these solutions with physical phenomena. In the field of neuroscience, the soliton hypothesis model asserts the initiation and conduction of action potentials along the axons based on the thermodynamics theory of wave pulse propagation. The current findings demonstrate that the approach is better suited to solving nonlinear evolution equations that arise in mathematical physics consistently.