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Analytical investigation of wave propagation and modulational instability in the fractional coupled Ramani equation
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DOI：10.1007/s11071-026-12868-z.png)
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Abstract
En 中文
The objective of manuscript is to investigate the nonlinear wave dynamics and modulational instability behavior of a fractional coupled Ramani-type equation with higher-order nonlinear and dispersive effects. The Fractional Reduced Differential Transform Method (FRDTM) is applied to evaluate analytical wave solutions of the governing fractional equation. Four distinct classes of nonlinear wave structures–cotangent-, hyperbolic cotangent, tangent, and hyperbolic tangent-type solutions–are successfully derived under appropriate initial conditions. A comprehensive modulational instability analysis is performed via linear perturbation theory, yielding an explicit nonlinear dispersion relation governing the instability mechanism. The key outcomes of investigation are as follows: (i) the modulational instability characteristics are found to be invariant across all obtained wave profiles, confirming that the instability dynamics are governed by the intrinsic nonlinear fractional structure of the model rather than the geometrical form of the solutions; (ii) fractional-order derivatives are shown to suppress perturbation growth rates and reduce instability bandwidths; and (iii) wave stability is significantly enhanced in the fractional regime compared to the corresponding classical integer-order model. These results give significant physical insights into the role of fractional dynamics in the control of nonlinear wave propagation and instability phenomena in complex dispersive systems.
Keywords:
Fractional coupled Ramani equation
Liouville–Caputo fractional derivative
Fractional Reduced Differential Transform Method
Modulational instability
Convergence analysis
Journal
IF:
6
Papers:
1.4W
Citations:
4.1W
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