Kinetics of phase separation in Fe–Cr–X (X =Mo, Cu) ternary alloys — a dynamical wave study

Abstract

Ternary alloys of Fe are very important materials having good corrosion resistance and are also famous for several high-temperature applications. The dynamical behavior of exact traveling waves for the kinetics of phase separation in Fe–Cr–X (X[Formula: see text]Mo, Cu) ternary alloys is modelled by convective-diffusive Cahn–Hilliard (CH) equation. A variety of nonlinear dynamical exact and solitary wave structures are extracted in several forms like rational, hyperbolic, trigonometric function solutions by the utilization of a sound computational integration tool, i.e., [Formula: see text]-model expansion method. Besides, we also secure mixed combined solitons and singular periodic wave solutions with unknown parameters. Moreover, the constraint conditions observed during derivation lead to substantial solutions. The findings elucidate that the governing model theoretically possesses significantly rich structures of exact traveling wave solutions. Hence, our technique via fortification of symbolic computations provides an active and potent mathematical implementation for solving diverse benevolent nonlinear wave problems.