initial value problem
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2022 ◽  
Vol 41 (1) ◽  
Silvio Antonio Bueno Salgado ◽  
Onofre Rojas ◽  
Sérgio Martins de Souza ◽  
Danilo Machado Pires ◽  
Leandro Ferreira

2022 ◽  
Vol 0 (0) ◽  
pp. 0
Marco Bravin ◽  
Luis Vega

<p style='text-indent:20px;'>In this note we study the initial value problem in a critical space for the one dimensional Schrödinger equation with a cubic non-linearity and under some smallness conditions. In particular the initial data is given by a sequence of Dirac deltas with different amplitudes but equispaced. This choice is motivated by a related geometrical problem; the one describing the flow of curves in three dimensions moving in the direction of the binormal with a velocity that is given by the curvature.</p>

Guoquan Qin ◽  
Zhenya Yan ◽  
Boling Guo

In this paper, we investigate the initial value problem of a nonlocal sine-type µ-Camassa-Holm (µCH) equation, which is the µ-version of the sine-type CH equation. We first discuss its local well-posedness in the framework of Besov spaces. Then a sufficient condition on the initial data is provided to ensure the occurance of the wave-breaking phenomenon. We finally prove the H¨older continuity of the data-to-solution map, and find the explicit formula of the global weak periodic peakon solution.

2021 ◽  
Vol 24 (4) ◽  
pp. 32-39
Hussein M. Sagban ◽  
Fadhel S. Fadhel ◽  

The main objective of this paper is to solve fuzzy initial value problems, in which the fuzziness occurs in the initial conditions. The proposed approach, namely the modified variational iteration method, will be used to find the solution of fuzzy initial value problem approximately and to increase the rate of convergence of the variational iteration method. From the obtained results, as it is expected, the approximate results of the proposed method are more accurate than those results obtained without using the modified variational iteration method.

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