Abstract
This work deals with the interaction of complex short wave envelope and real long wave described by the coupled Schrödinger–Boussinesq equation with variable-coefficients and beta space fractional evolution. The above interacting wave phenomena are studied by evaluating new non-autonomous analytical solutions of the considered coupled equation. The solutions of the equations are obtained by modifying the auxiliary ordinary differential equation method and taking the conformable beta derivative properties into account. The behaviors of the resonance nonautonomous structures are discussed with physical insight for diverse consideration of the chance functions of time-dependent in the solutions.
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