87 citations · 192 across the 23 of their papers we have counts for
28 papers
Error bounds for Physics Informed Neural Networks in Nonlinear Schrödinger equations placed on unbounded domains
Miguel Á. Alejo, Lucrezia Cossetti, Luca Fanelli +2
We consider the subcritical nonlinear Schrödinger (NLS) in dimension one posed on the unbounded real line. Several previous works have considered the deep neural network approximat…
Nonlinear Stability of nonsingular solitons of the Principal Chiral Field equation
Miguel Á. Alejo, Claudio Muñoz, Jessica Trespalacios
We consider the Principal Chiral Field model posed in 1+1 dimensions into the Lie group . In this work we show the nonlinear stability of small enough nonsi…
On the nonexistence of NLS breathers
Miguel Á. Alejo, Adán J. Corcho
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 nonex…
Stability of mKdV breathers on the half-line
Miguel A. Alejo, Márcio Cavalcante, Adán J. Corcho
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 orig…
Breather Solutions to the Cubic Whitham Equation
Henrik Kalisch, Miguel A. Alejo, Adán J. Corcho +1
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 str…
Decay for Skyrme wave maps
Miguel A. Alejo, Christopher Maulén
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 Ad…
Review on the stability of the Peregrine and related breathers
Miguel A. Alejo, Luca Fanelli, Claudio Muñoz
In this note, we review stability properties in energy spaces of three important nonlinear Schrödinger breathers: Peregrine, Kuznetsov-Ma, and Akhmediev. More precisely, we show th…
On the asymptotic stability of the sine-Gordon kink in the energy space
Miguel A. Alejo, Claudio Muñoz, José M. Palacios
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 . It is well-known…
Orbital stability of the black soliton for the quintic Gross-Pitaevskii equation
Miguel A. Alejo, Adán J. Corcho
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…
Dynamics of breathers in the Gardner hierarchy: universality of the variational characterization
Miguel A. Alejo, Eleomar Cardoso
We present a new variational characterization of breather solutions of any equation of the \emph{focusing} Gardner hierarchy. This hierarchy is characterized by a nonnegative index…
Global solutions and stability properties of the 5th order Gardner equation
Miguel A. Alejo, Chulkwang Kwak
In this work, we deal with the initial value problem of the 5th-order Gardner equation in , presenting the local well-posedness result in . As a conseq…
Stability and instability of breathers in the Sasa-Satusuma and Nonlinear Schrödinger models
Miguel A. Alejo, Luca Fanelli, Claudio Muñoz
We consider the Sasa-Satsuma (SS) and Nonlinear Schrödinger (NLS) equations posed along the line, in 1+1 dimensions. Both equations are canonical integrable models, with sol…
On global solutions to some non-Markovian quantum kinetic models of Fokker-Planck type
Miguel A. Alejo, José Luis López
In this paper, global well-posedness of the non-Markovian Unruh-Zurek and Hu-Paz-Zhang master equations with nonlinear electrostatic coupling is demonstrated. They both consist of…
On the dynamics of zero-speed solutions for Camassa-Holm type equations
Miguel A. Alejo, Manuel F. Cortez, Chulkwang Kwak +1
In this paper we consider globally defined solutions of Camassa-Holm (CH) type equations outside the well-known nonzero speed, peakon region. These equations include the standard C…
The Akhmediev Breather is unstable
Miguel A. Alejo, Luca Fanelli, Claudio Muñoz
In this note, we give a rigorous proof that the NLS periodic Akhmediev breather is unstable. The proof follows the ideas in [17], in the sense that a suitable modification of the S…
On the ill-posedness of the 5th-order Gardner equation
Miguel A. Alejo, Eleomar Cardoso
We present ill-posedness results for the initial value problem (IVP) of the 5th-order Gardner equation. We use new breather solutions discovered for this higher order Gardner equat…
Nonlinear stability of higher order mKdV breathers
Miguel A. Alejo, Eleomar Cardoso
We are interested in stability results for breather solutions of the 5th, 7th and 9th order mKdV equations. We show that these higher order mKdV breathers are stable in ,…
Almost sharp nonlinear scattering in one-dimensional Born-Infeld equations arising in nonlinear Electrodynamics
Miguel A. Alejo, Claudio Muñoz
We study decay of small solutions of the Born-Infeld equation in 1+1 dimensions, a quasilinear scalar field equation modeling nonlinear electromagnetism, as well as branes in Strin…
Nonlinear stability of Gardner breathers
Miguel A. Alejo
We show that breather solutions of the Gardner equation, a natural generalization of the KdV and mKdV equations, are stable. Through a variational approach, we ch…
Collective Coordinates Theory for Discrete Soliton Ratchets in the sine-Gordon Model
B. Sánchez-Rey, N. R. Quintero, J. Cuevas-Maraver +1
A collective coordinate theory is develop for soliton ratchets in the damped discrete sine-Gordon model driven by a biharmonic force. An ansatz with two collective coordinates, nam…
On the variational structure of breather solutions
Miguel A. Alejo, Claudio Muñoz, José M. Palacios
In this paper we give a systematic and simple account that put in evidence that many breather solutions of integrable equations satisfy suitable variational elliptic equations, whi…
Dynamics of complex-valued modified KdV solitons with applications to the stability of breathers
Miguel Angel Alejo, Claudio Muñoz
We study the long-time dynamics of complex-valued modified Korteweg-de Vries (mKdV) solitons, which are recognized because they blow-up in finite time. We establish stability prope…
Nonlinear stability of mKdV breathers
Miguel Angel Alejo, Claudio Muñoz
Breather solutions of the modified Korteweg-de Vries equation are shown to be globally stable in a natural H^2 topology. Our proof introduces a new Lyapunov functional, at the H^2…
On the nonlinear stability of mKdV breathers
Miguel Angel Alejo, Claudio Muñoz
A mathematical proof for the stability of mKdV breathers is announced. This proof involves the existence of a nonlinear equation satisfied by all breather profiles, and a new Lyapu…