Approximate Analytical Solution of the Nonlinear Bethe Equation

摘要: Bethe equation is a nonlinear differential that appears in nuclear physics and plays an important role various applications ranging from basic science to engineering medicine. Please confirm the corresponding author correctly identified amend if necessary. It describes behavior of charged particle when it enters material medium. Despite its importance, unusual find exact solutions for this non-linear literature practically all related studies focus on contrasting predictions given by approximate with experiments. In work, we solve approximately present new approach obtain solution through combined use Adomian Decomposition Method Laplace Transform (LADM). Additionally, illustrate our solving some examples which initial conditions are considered within numerical ranges typical experimental situations. Our results indicate LADM highly accurate can be as very useful valuable method study equation.