Solving a nonlinear Modified Burgers' equation with a forcing term using a new Parametric Sinh-Method
In this work, we explore a nonlinear Modified Burgers' Equation (MBE) which is constructed by introducing an initially unknown forcing term. Modeled after the previously established Tanh-method, the "Parametric Sinh-Method" is conceived from a parametric ansatz possessing both hyperbolic tangent and hyperbolic sine forms on its terminals. A rigorous demonstration of the new Parametric Sinh-Method is performed, aiming to to solve the exact forcing term and corresponding solution to the MBE. Ultimately, a unique MBE+Solution pair is determined, offering a potential for further analysis.