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of 246
pro vyhledávání: '"Adán, J."'
The initial value problem (IVP) for the non-isotropic Schr\"odinger equation posed on the two-dimensional cylinders and $\mathbb{T}^2$ is considered. The IVP is shown to be locally well-posed for small initial data in $H^s(\mathbb{T}\times\mathbb{R})
Externí odkaz:
http://arxiv.org/abs/2411.01392
Autor:
Alejo, Miguel Á., Corcho, Adán J.
In this work, a rigorous proof of the nonexistence of breather solutions for NLS equations is presented. By using suitable virial functionals, we are able to characterize the nonexistence of breather solutions, different from standing waves, by only
Externí odkaz:
http://arxiv.org/abs/2408.09862
In this paper we study the stability problem for mKdV breathers on the left half-line. We are able to show that leftwards moving breathers, initially located far away from the origin, are strongly stable for the problem posed on the left half-line, w
Externí odkaz:
http://arxiv.org/abs/2206.02898
We are concerned with numerical approximations of breather solutions for the cubic Whitham equation which arises as a water-wave model for interfacial waves. The model combines strong nonlinearity with the non-local character of the water-wave proble
Externí odkaz:
http://arxiv.org/abs/2201.12074
Publikováno v:
In Journal of Computational and Applied Mathematics 1 May 2025 460
Autor:
Corcho, Adán J., Cordero, Juan C.
In this paper we show that solutions of the cubic nonlinear Schr\"odinger equation are asymptotic limit of solutions to the Benney system. Due to the special characteristic of the one-dimensional transport equation same result is obtained for solutio
Externí odkaz:
http://arxiv.org/abs/2006.13874
Autor:
Alejo, Miguel A., Corcho, Adán J.
In this work, a rigorous proof of the orbital stability of the black soliton solution of the quintic Gross-Pitaevskii equation in one spatial dimension is obtained. We first build and show explicitly black and dark soliton solutions and we prove that
Externí odkaz:
http://arxiv.org/abs/2003.09994
Publikováno v:
In Applied Numerical Mathematics January 2023 183:355-368
Asymptotic behavior of the Schr\'odinger-Debye system with refractive index of square wave amplitude
Autor:
Corcho, Adan J., Cordero, Juan C.
We obtain local well-posedness for the one-dimensional Schr\"odinger-Debye interactions in nonlinear optics in the spaces $L^2\times L^p,\; 1\le p < \infty$. When $p=1$ we show that the local solutions extend globally. In the focusing regime, we cons
Externí odkaz:
http://arxiv.org/abs/1705.01003
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