The direct method proposed by Clarkson and Kruskal is modified to obtain some conditional similarity solutions of a nonlinear physics model. Taking the -dimensional Boussinesq equation as a simple example, six types o...The direct method proposed by Clarkson and Kruskal is modified to obtain some conditional similarity solutions of a nonlinear physics model. Taking the -dimensional Boussinesq equation as a simple example, six types of conditional similarity reductions are obtained.展开更多
Using every realization of the Virasoro-type symmetry algebra , we can obtain various high-dimensional integrable models under the meaning that they possess infinitely many symmetries. By means of a concrete realizati...Using every realization of the Virasoro-type symmetry algebra , we can obtain various high-dimensional integrable models under the meaning that they possess infinitely many symmetries. By means of a concrete realization, many -dimensional equations which possess Kac–Moody–Virasoro-type infinite dimensional symmetry algebras are obtained.展开更多
We consider a simple collinear collision ofa 'classical' particle with a harmonic oscillator within quantum semiclassical model and full quantum dynamics model, in which the latter is solved analytically in sq...We consider a simple collinear collision ofa 'classical' particle with a harmonic oscillator within quantum semiclassical model and full quantum dynamics model, in which the latter is solved analytically in squeezed state and exact diagonalization methods and acts as the exact solution of such a system. A comparison of these two models for different mass ratios between the 'classical' particle and the quantum particle is done, which gives a criterion when using the quantum-semiclassical model.展开更多
文摘The direct method proposed by Clarkson and Kruskal is modified to obtain some conditional similarity solutions of a nonlinear physics model. Taking the -dimensional Boussinesq equation as a simple example, six types of conditional similarity reductions are obtained.
文摘Using every realization of the Virasoro-type symmetry algebra , we can obtain various high-dimensional integrable models under the meaning that they possess infinitely many symmetries. By means of a concrete realization, many -dimensional equations which possess Kac–Moody–Virasoro-type infinite dimensional symmetry algebras are obtained.
文摘We consider a simple collinear collision ofa 'classical' particle with a harmonic oscillator within quantum semiclassical model and full quantum dynamics model, in which the latter is solved analytically in squeezed state and exact diagonalization methods and acts as the exact solution of such a system. A comparison of these two models for different mass ratios between the 'classical' particle and the quantum particle is done, which gives a criterion when using the quantum-semiclassical model.
