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Articles 1 - 4 of 4
Full-Text Articles in Physical Sciences and Mathematics
Converting Fractional Differential Equations Into Partial Differential Equations, Ji-Huan He, Zheng-Biao Li
Converting Fractional Differential Equations Into Partial Differential Equations, Ji-Huan He, Zheng-Biao Li
Ji-Huan He
A transform is suggested in this paper to convert fractional differential equations with the modified Riemann-Liouville derivative into partial differential equations, and it is concluded that the fractional order in fractional differential equations is equivalent to the fractal dimension.
A Historical Scientific Announcement On Dark Energy, Ji-Huan He
A Historical Scientific Announcement On Dark Energy, Ji-Huan He
Ji-Huan He
he mysterious secret of dark energy will be revealed in the mini-symposium on dark energy of 2012 ISND on Oct.30, 2012 at Galaxy Hotel, Shanghai, China
Hamiltonian Approach To Solitary Solutions, Ji-Huan He
Hamiltonian Approach To Solitary Solutions, Ji-Huan He
Ji-Huan He
A variational principle is established for a nonlinear wave equation, and its Hamiltonian invariant can be readily obtained. An asymptotic approach to solitary solution is proposed based on the obtained Hamiltonian. The KdV equation is used as an example to elucidate the solution procedure, and the exact solitary solution is obtained, showing the effectiveness of the novel method.
Asymptotic Methods For Solitary Solutions And Compactons, Ji-Huan He
Asymptotic Methods For Solitary Solutions And Compactons, Ji-Huan He
Ji-Huan He
This review is an elementary introduction to some new asymptotic methods for the search for the solitary solutions of nonlinear differential equations, nonlinear differential-difference equations, and nonlinear fractional differential equations . Particular attention is paid throughout the paper to giving an intuitive grasp for the variational approach, the Hamiltonian approach, the variational iteration method, the homotopy perturbation method, the parameter-expansion method, the Yang-Laplace Transform, the Yang-Fourier transform, and ancient Chinese mathematics. Hamilton principle and variational principles are also emphasized. The reviewed asymptotic methods are easy to be followed for various applications. Some ideas on this review article are first appeared. …