Lie symmetry analysis, new group invariant for the (3 + 1)-dimensional and variable coefficients for liquids with gas bubbles models

A Numerical Investigation Based on Exponential Collocation Method for Nonlinear SITR Model of COVID-19

“…Each equation is describing the transmission behavior of individuals in the respective compartments. By this transmission number of individuals can vary in each of the five compartments [22][23][24][25][26][27][28][29][30]. The description of the transition rates in each cell is given in Table 2.…”

Sistema óptimo, soluciones invariantes y clasificación completa del grupo de simetrías de Lie para la ecuación de Kummer-Schwarz generalizada y su representación del álgebra de Lie

“…Taking into account [15,17,35,42], we present in this section the optimal algebra associated to the symmetry group of (1), that shows a systematic way to classify the invariant solutions.…”

“…Thus, in [20] the following solutions are proposed for (1) y(x) = 1 x and y(x) = −x, (5) these solutions are calculated using the method presented by Hydon [14], which proposes how to find a complete list of all discrete symmetry groups for a differential equation and its possible solutions. In [41], Polyanin and Zaitsev presented the following differential equation y xxx = A (y x ) −1 (y xx ) 2 , where A ̸ = 1, 2 is a constant.…”

“…The objective of our work is: i) to provide a complete classification of Lie symmetries group for (2), ii) to present the optimal system (optimal algebra) for (1), iii) making use of all elements of the optimal algebra, to propose invariant solutions for (1) different from ( 5) and ( 8), finally iv) to classify the Lie algebra associated to (1), corresponding to the Lie symmetry group.…”

“…Recently, the Lie group method approach has been applied to solve and analyze different problems in many scientific fields, e.g., in [25], the authors applied the Lie symmetry method to investigate some solutions for pZK equation, which models the nonlinear propagation of dust-ion acoustic solitary waves and shocks, and in [11] the authors studied the invariance of stochastic differential equations under random diffeomorphisms and established the determining equations for random Lie point symmetries of stochastic differential equations. Some references in the latest progress using Lie group symmetries can be found in [1,10,13,27,37,40] and references therein, some recent publications in the area of Lie symmetry groups, optimal system, and invariant solutions can be found in [2,21,22,23,24,30,31,38].…”