Physics

Nonlinear system

Trigonometry

Mathematics

Sine wave

Limit (mathematics)

Mathematical analysis

Voltage

Trigonometric functions

Sine

Geometry

Exact solutions in general relativity

Quantum mechanics

Hyperbolic function

Traveling wave

Periodic wave

Rational function

Physica Scripta

Solitonic solutions have become a popular topic among traveling wave solutions since they act as a bridge between mathematics and physics. In this article, two newly developed methods, namely the extended rational sine-cosine method and extended rational sinh-cosh method by means of fractional complex transform are applied to construct the exact solutions in the form of hyperbolic, trigonometric and rational functions of the nonlinear fractional Phi-4 equation. The obtained solutions are further expressed by solitons, dark solitons, periodic and kink wave solutions. The proposed methods analyze the possibility of the existence of limit cycles with specific parameters.

Exact solitary wave solutions by extended rational sine-cosine and extended rational sinh-cosh techniques