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The homogeneous balance of undetermined coefficients method and its application

100%

Wei Y., He X.-D., Yang X.-F.

Open Mathematics

2016

tom 14

nr 1

816-826

The homogeneous balance of undetermined coefficients method is firstly proposed to solve such nonlinear partial differential equations (PDEs), the balance numbers of which are not positive integers. The proposed method can also be used to derive more general bilinear equation of nonlinear PDEs. The Eckhaus equation, the KdV equation and the generalized Boussinesq equation are chosen to illustrate the validity of our method. The proposed method is also a standard and computable method, which can be generalized to deal with some types of nonlinear PDEs.

On the derivation and mathematical analysis of some quantum–mechanical models accounting for Fokker–Planck type dissipation: Phase space, Schrödinger and hydrodynamic descriptions

52%

López J. L., Montejo–Gámez J.

Nanoscale Systems: Mathematical Modeling, Theory and Applications

2013

tom 2

49-80

This paper is intended to provide the reader with a review of the authors’ latest results dealing with the modeling of quantum dissipation/diffusion effects at the level of Schrödinger systems, in connection with the corresponding phase space and fluid formulations of such kind of phenomena, especially in what concerns the role of the Fokker–Planck mechanism in the description of open quantum systems and the macroscopic dynamics associated with some viscous hydrodynamic models of Euler and Navier–Stokes type.

Ograniczanie wyników

1 Nanoscale Systems: Mathematical Modeling, Theory and Applications

1 Open Mathematics

1 He X.-D.

1 López J. L.

1 Montejo–Gámez J.

1 Wei Y.

1 Yang X.-F.

1 2016

1 2013

Wyniki wyszukiwania

The homogeneous balance of undetermined coefficients method and its application

On the derivation and mathematical analysis of some quantum–mechanical models accounting for Fokker–Planck type dissipation: Phase space, Schrödinger and hydrodynamic descriptions