Analytical solutions of the space–time fractional Kundu–Eckhaus equation by using modified extended direct algebraic method

Abstract

The study of soliton solutions for Nonlinear Fractional Partial Differential Equations (NFPDEs) has gained prominence recently because of its ability to realistically recreate complex physical processes. Numerous mathematical techniques have been devised to handle the problem of NFPDEs where soliton solutions are difficult to obtain. Due to their accuracy in reproducing complex physical phenomena, soliton solutions for Nonlinear Fractional Partial Differential Equations (NFPDEs) have recently attracted interest. Several mathematical techniques have been devised to tackle the difficult task of solving non-finite partial differential equations (NFPDEs) soliton. Studies of soliton solutions for Nonlinear Fractional Partial Differential Equations (NFPDEs) have garnered increased attention recently due to its capacity to accurately represent complex physical processes. Due to the difficulty of obtaining soliton solutions, NFPDEs can be solved using a wide variety of mathematical methods. In this way, it facilitates the extraction of the recently found abundance of optical soliton solutions. To further understanding of the results, the study also includes contour and three-dimensional images that visually depict particular optical soliton solutions for particular parameter selections, suggesting the existence of different soliton structures in the nonlinear fractional Kundu–Eckhaus equation (NFKEE) region. It is shown that the proposed technique is quite powerful and effective in solving several nonlinear FDEs.

Keywords

• Nonlinear Fractional partial differential equations (NFPDEs)
• Space–time fractional Kundu–Eckhaus equation
• Extended direct algebraic method (EDAM)
• Solitary wave solutions
• Nonlinear ordinary differential equations (NODE)
• Variable transformation