Zobrazeno 1 - 10
of 123
pro vyhledávání: '"Alejo, Miguel A."'
We consider the subcritical nonlinear Schr\"odinger (NLS) in dimension one posed on the unbounded real line. Several previous works have considered the deep neural network approximation of NLS solutions from the numerical and theoretical point of vie
Externí odkaz:
http://arxiv.org/abs/2409.17938
We consider the Principal Chiral Field model posed in 1+1 dimensions into the Lie group $\text{SL}(2,\mathbb R)$. In this work we show the nonlinear stability of small enough nonsingular solitons. The method of proof involves the use of vector field
Externí odkaz:
http://arxiv.org/abs/2408.09969
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
Autor:
Alejo, Miguel A., Maulén, Christopher
We consider the decay problem for global solutions of the Skyrme and Adkins-Nappi equations. We prove that the energy associated to any bounded energy solution of the Skyrme (or Adkins-Nappi) equation decays to zero outside the light cone (in the rad
Externí odkaz:
http://arxiv.org/abs/2108.01163
Autor:
Alejo, Miguel Á.1 malejo@uco.es
Publikováno v:
Proyecciones - Journal of Mathematics. Apr2024, Vol. 43 Issue 2, p495-520. 26p.
In this note, we review stability properties in energy spaces of three important nonlinear Schr\"odinger breathers: Peregrine, Kuznetsov-Ma, and Akhmediev. More precisely, we show that these breathers are unstable according to a standard definition o
Externí odkaz:
http://arxiv.org/abs/2008.11590
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
We consider the sine-Gordon (SG) equation in 1+1 dimensions. The kink is a static, non-symmetric exact solution to SG, stable in the energy space $H^1\times L^2$. It is well-known that the linearized operator around the kink has a simple kernel and n
Externí odkaz:
http://arxiv.org/abs/2003.09358