Ginzburg–Landau equations involving different effects and their solitary waves

Ginzburg–Landau (GL) equations describe a wide range of phenomena involving superconductivity, superfluidity, etc. In the present paper, Ginzburg–Landau equations involving distinct laws are considered, and as a consequence, their solitary waves in the presence of perturbation terms are formally derived using the Kudryashov method. The effect of Kerr and parabolic laws on the dynamics of solitary waves is examined in detail. The outcomes of the current paper present suitable ways to control the width and amplitude of solitary waves. The authors believe that the results reported in the current study will contribute significantly to studies related to Ginzburg–Landau equations with distinct laws.