Existence of exotic waves for the nonlinear dispersive mKdV equation

Yin, Jiuli; Ding, Shanyu; Li, Tian; Fan, Xinghua; Deng, Xinyang

doi:10.1016/j.amc.2013.12.043

Cited by 2 publications

(1 citation statement)

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“…The problem of wave-wave interaction is a very important one in the earth fluid, and further study can deepen people's understanding of large-scale motion phenomena in the atmosphere, ocean and large lakes. There are many motion equations describing Rossby waves in a layer of fluid, such as one-dimensional KdV equation [13], MKdV equation [14], Boussinesq equation [15] and high-dimensional ZK equation [16], mZK equation [17], KP equation [18] and so on. The actual atmospheric ocean system is very complex, compared with the single equation of low dimension, the coupled equations set [19][20][21]of high dimension are more practical.…”

Section: Introductionmentioning

confidence: 99%

Time-Space Fractional Coupled Generalized Zakharov-Kuznetsov Equations Set for Rossby Solitary Waves in Two-Layer Fluids

Chen

Yang

2019

Mathematics

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In this paper, the theoretical model of Rossby waves in two-layer fluids is studied. A single quasi-geostrophic vortex equation is used to derive various models of Rossby waves in a one-layer fluid in previous research. In order to explore the propagation and interaction of Rossby waves in two-layer fluids, from the classical quasi-geodesic vortex equations, by employing the multi-scale analysis and turbulence method, we derived a new (2+1)-dimensional coupled equations set, namely the generalized Zakharov-Kuznetsov(gZK) equations set. The gZK equations set is an extension of a single ZK equation; they can describe two kinds of weakly nonlinear waves interaction by multiple coupling terms. Then, for the first time, based on the semi-inverse method and the variational method, a new fractional-order model which is the time-space fractional coupled gZK equations set is derived successfully, which is greatly different from the single fractional equation. Finally, group solutions of the time-space fractional coupled gZK equations set are obtained with the help of the improved ( G ′ / G ) -expansion method.

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