Abstract
This paper explores the interactions of capillary–gravity waves by presenting novel exact solutions to a coupled Schrödinger–KdV equation. The authors introduce a reduction method based on Nucci’s approach to derive these exact solutions. The results provide a new approach to solving the Schrödinger–KdV equation, offering potential applications in various fields such as mathematical physics, hydrodynamics, and soliton theory. Effectiveness and versatility of utilized reduction technique make it a valuable tool for researchers in various fields, including mathematical physics, fluid mechanics, and nonlinear dynamics. Overall, this research contributes to the understanding of the complex behavior of capillary–gravity waves and provides a useful tool for modeling and analyzing such phenomena.
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Notes
It’s noteworthy that in case 1, we made the assumption that \(k=\frac{{\sigma }^{2}}{4}+\frac{\sigma }{24}\), or in other words, \(\sigma =-\frac{1\pm \sqrt{1+576,k}}{12}\). However, in this case, the assumption is \(\sigma =-\frac{1+\sqrt{1+576,k}}{12}\). The difference between the two assumptions still applies to the remaining parameters. Essentially, we divided the ± sign, into two separate cases.
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MSH, developed the theory and performed the computations. AMW: verified the analytical methods and supervised the findings of this work.
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Hashemi, M.S., Wazwaz, AM. Novel exact solutions to a coupled Schrödinger–KdV equations in the interactions of capillary–gravity waves. Opt Quant Electron 55, 567 (2023). https://doi.org/10.1007/s11082-023-04826-5
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DOI: https://doi.org/10.1007/s11082-023-04826-5