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BLOW-UP OF SOLUTIONS OF NONLINEAR SCHRODINGER EQUATIONS WITH OSCILLATING NONLINEARITIES
The finite time blow-up of solutions for 1-D NLS with oscillating nonlinearities is shown in two domains: (1) the whole real line where the nonlinear source is acting in the interior of the domain and (2) the right half-line where the nonlinear source is placed at the boundary point. The distinctive feature of this work is that the initial energy is allowed to be non-negative and the momentum is allowed to be infinite in contrast to the previous literature on the blow-up of solutions with time dependent nonlinearities. The common finite momentum assumption is removed by using a compactly supported or rapidly decaying weight function in virial identities - an idea borrowed from . At the end of the paper, a numerical example satisfying the theory is provided.
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Korkut Uysal, Sıla Övgü (Izmir Institute of Technology, 2015-06)This thesis proposes two different numerical methods for solving nonlinear oscillation problems which appear in engineering and physics. Thus, the study is conducted in two parts. The first part introduces and analyzes ...
Various real world phenomena such as optical communication channels, power amplifiers and movement of sea vessels exhibit nonlinear characteristics. The nonlinearity degree of such systems is assumed to be known as a general ...
By generating function based on Jackson's q-exponential function and the standard exponential function, we introduce a new q-analogue of Hermite and Kampe-de Feriet polynomials. In contrast to q-Hermite polynomials with ...