Physically significant solitary wave solutions to the space-time fractional Landau–Ginsburg–Higgs equation via three consistent methods

Abstract

The Landau–Ginzburg–Higgs equation (LGHE) is a mathematical model used to describe nonlinear waves that exhibit weak scattering and long-range connections in the tropical and mid-latitude troposphere as interactions between equatorial and mid-latitude Rossby waves. This study assessed the fractional Landau–Ginzburg–Higgs model, previously introduced in truncated M-fractional derivatives utilizing the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m1"><mml:mrow><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:msup><mml:mi>G</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mo>/</mml:mo><mml:mi>G</mml:mi><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mi>G</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:math> , modified <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m2"><mml:mrow><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:msup><mml:mi>G</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mo>/</mml:mo><mml:msup><mml:mi>G</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:mfenced></mml:mrow></mml:math> , and new auxiliary equation methods. Using these techniques, different solutions, including unknown parameters, were obtained in trigonometric, hyperbolic, and exponential functions. This study investigated how varying values of the fractional parameter affected the deeds of the solutions obtained for the given conditions. The predicted solutions, obtained under restricted conditions, were visualized through 2D, 3D, and contour plots using appropriate parameter values. The attained results were confirmed for the aforementioned equations using symbolic soft computations. Moreover, the outcomes confirmed that the methods used in this study were effective mathematical tools for discovering exact solitary wave solutions to nonlinear models encountered in various areas of science and engineering.

Topics & Concepts