De Broglie waves and nuclear element interaction; Abundant waves structures of the nonlinear fractional Phi-four equation

Abstract

This research study investigates the computational wave solutions of the nonlinear fractional Phi-four (NLFPF) equation. The NLFPF model describes the nuclear element interaction and is also a very effective unique form of the Klein–Gordon (KG) equation. Two recent analytical (Khater II (Khat II) and Novel Kudryashov (NKud)) schemes are applied to the NLFPF model for constructing some novel solitary wave solutions. These solutions are explained through some numerical simulation to explain more properties of the nuclear element interaction. The paper’s novelty, scientific contributions, and results’ physical explanations are demonstrated. All solutions’ accuracy has been checked by putting them back into the original model by using Mathematica 13.1.