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Full-Text Articles in Non-linear Dynamics
Singularities And Global Solutions In The Schrodinger-Hartree Equation, Anudeep Kumar
Singularities And Global Solutions In The Schrodinger-Hartree Equation, Anudeep Kumar
FIU Electronic Theses and Dissertations
In 1922, Louis de Broglie proposed wave-particle duality and introduced the idea of matter waves. In 1925, Erwin Schrodinger, proposed a wave equation for de Broglie’s matter waves. The Schrodinger equation is described using the de Broglie’s matter wave, which takes the wave function, and describes its quantum state over time.
Herein, we study the generalized Hartree (gHartree) equation, which is a nonlinear Schrodinger type equation except now the nonlinearities are a nonlocal (convolution) type. In the gHartree equation, the influence on the behavior of the solutions is global as opposed to the case of local (power type) nonlinearities.
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