부산대학교 도서관

Summary: ``This paper investigates nonlinear wave-wave interactions ina system that describes a modified decay instability and consists ofthree Langmuir and one ion-sound waves. As a means to establish thatthe underlying dynamics exists in a 3D space and that it is of theLorenz-type, both continuous and discrete-time multivariable globalmodels were obtained from data. These data were obtained from a 10Ddynamical system that describes the modified decay instabilityobtained from Zakharov's equations which characterise Langmuirturbulence. This 10D model is equivariant under a continuous rotationsymmetry and a discrete order-2 rotation symmetry. When the continuousrotation symmetry is modded out, that is, when the dynamics arerepresented with the continuous rotation symmetry removed under alocal diffeomorphism, it is shown that a 3D system may describe theunderlying dynamics. For certain parameter values, the models,obtained using global modelling techniques from three time series fromthe 10D dynamics with the continuous rotation symmetry modded out,generate attractors which are topologically equivalent. These modelscan be simulated easily and, due to their simplicity, are amenable foranalysis of the original dynamics after symmetries have been moddedout. Moreover, it is shown that all of these attractors aretopologically equivalent to an attractor generated by the well-knownLorenz system.''