Lie Symmetry Analysis of the Nonlinear Schrödinger Equation with Time Dependent Variable Coefficients

Application of Lie Group-based Neural Network Method to Nonlinear Dynamical Systems

“…where x is the dependent variable representing the density of the bottom prey population, y is the dependent variable representing the density of the middle predator(prey) population, z is the dependent variable representing the density of the higher predator population, and t is the independent variable representing time, which is ǫ in (20), the initial conditions are x(0) = 0.5, y(0) = 1, z(0) = 2, and we consider the case where t is in the interval [0, 3]. In the absence of a predator (y = 0), Eq.…”

“…Lie group is vital to understanding the solutions characteristics of a nonlinear DEs since it provides a reasonable framework for analysing the solutions to the DEs. For further information on Lie groups of a DEs, one refers to see [17][18][19][20]. Best in our knowledge, the essential combination of Lie group method, a powerful theoretical and computational tool, and NN method has not yet explored so far.…”

Approximate Nonlocal Symmetries for a Perturbed Schrödinger Equation with a Weak Infinite Power-Law Memory

“…In [46], approximate symmetries for a perturbed nonlinear equation have been studied. For some more recent results on symmetry analysis we refer to recent papers [47][48][49].…”