Abundant Exact Soliton Solutions to the Space-Time Fractional Phi-Four Effective Model for Quantum Effects Through the Modern Scheme

  • M. Al-Amin Department of Mathematics, Islamic University, Kushtia, Bangladesh
  • M. Nurul Islam Department of Mathematics, Islamic University, Kushtia, Bangladesh
  • M. Ali Akbar Department of Applied Mathematics, University of Rajshahi, Bangladesh
Keywords: The Phi-4 model, the auxiliary equation method, nonlinear evolution equation, soliton


The space-time fractional Phi-four (PF) equation is measured as a particular case of the familiar Klein-Fock-Gordon (KFG) model and plentiful quantum effects can be investigated through the PF model’s solutions. In this article, the auxiliary equation method (AEM) is employed to attain the traveling wave solutions and in this purpose, the complex wave transformation and Maple software are utilized. The constructed wave solutions are the form likely, hyperbolic, exponential, rational, and trigonometric functions as well as their integration. The physical significance of the obtained solutions for the specific values of the integrated parameters in the course of representing graphs and understood the physical phenomena. It is shown that the AEM is powerful, effective and simple and provide more general traveling wave solutions to the NLEEs.


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