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In this chapter, the M-fractional generalized coupled nonlinear Schrödinger–Korteweg–de Vries (NLS-KdV) equations which arise as an equation for the interaction between long and short nonlinear waves are investigated. The Jacobi elliptic function (JEF) solutions are found using the modified Jacobi elliptic expansion method. In special cases, dark and bright soliton solutions to the system are retrieved when the modulus of Jacobi elliptic function approaches unity. A comparative analysis is represented by graphically to study the effect of the fractional order on the obtained solutions. In addition, the modulation instability of the equation is investigated by using the standard linear stability analysis. The influence of various parameters on modulation instability gain is discussed graphically.

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The M-Fractional Generalized Long-Short Wave Interaction System: Soliton Solutions and Stability Analysis

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  • 发表日期：

    2025年

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  • Thilagarajah Mathanaranjan

摘要

In this chapter, the M-fractional generalized coupled nonlinear Schrödinger–Korteweg–de Vries (NLS-KdV) equations which arise as an equation for the interaction between long and short nonlinear waves are investigated. The Jacobi elliptic function (JEF) solutions are found using the modified Jacobi elliptic expansion method. In special cases, dark and bright soliton solutions to the system are retrieved when the modulus of Jacobi elliptic function approaches unity. A comparative analysis is represented by graphically to study the effect of the fractional order on the obtained solutions. In addition, the modulation instability of the equation is investigated by using the standard linear stability analysis. The influence of various parameters on modulation instability gain is discussed graphically.