In nonlinear optics, fluid mechanics, plasma physics or atmospheric science: symbolic computation on a generalized variable-coefficient Korteweg-de Vries equation

Studies in nonlinear optics, fluid mechanics, plasma physics and atmospheric science are of current interest. In nonlinear optics, fluid mechanics, plasma physics or atmospheric science, we investigate a generalized variable-coefficient Korteweg-de Vries equation. With respect to the wave amplitude, we construct two sets of the similarity reductions, each of which comes to a known ordinary differential equation. Our results rely on the variable coefficients in the equation.

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This article discusses the importance of studying nonlinear optics, fluid mechanics, plasma physics, and atmospheric science. It explores a generalized variable-coefficient Korteweg-de Vries equation and presents the construction of similarity reductions for two sets of wave amplitudes, resulting in known ordinary differential equations. The results are dependent on the variable coefficients in the equation.