In the last 60 years, there was formed a universal nonlinear analysis, whose unified algorithms allow to find asymptotic forms and asymptotic expansions of solutions to nonlinear equations and systems of different types: algebraic, ordinary differential (ODE), partial differential (PDE) and systems of mixed-type equations. This calculus contains two main algorithms: (a) Reducing equations to the normal form and (b) Separating truncated equations, and two kinds of transformations of coordinate can be used to simplify the obtained equations: (A) Power and (B) Logarithmic. Here we show that for algebraic equation, single ODE, autonomous system of ODE’s, Hamiltonian system, single PDE. Some applications are mentioned as well.
In the last 60 years, there was formed a universal nonlinear analysis, whose unified algorithms allow to find asymptotic forms and asymptotic expansions of solutions to nonlinear equations and systems of different types: algebraic, ordinary differential (ODE), partial differential (PDE) and systems of mixed-type equations. This calculus contains two main algorithms: (a) Reducing equations to the normal form and (b) Separating truncated equations, and two kinds of transformations of coordinate can be used to simplify the obtained equations: (A) Power and (B) Logarithmic. Here we show that for algebraic equation, single ODE, autonomous system of ODE’s, Hamiltonian system, single PDE. Some applications are mentioned as well.