Studies on a system of nonlinear Schrödinger equations with potential and quadratic interaction
Sign Up to like & getrecommendations! Published in 2024 at "Mathematische Nachrichten"
DOI: 10.1002/mana.202400068
Abstract: In this work, we study the existence of various classes of standing waves for a nonlinear Schrödinger system with quadratic interaction, along with a harmonic or partially harmonic potential. We establish the existence of ground‐state… read more here.
Keywords: quadratic interaction; system; schr dinger; nonlinear schr ... See more keywords
Traveling waves for a nonlinear Schrödinger system with quadratic interaction in ℝ4$$ {\mathrm{\mathbb{R}}}^4 $$
Sign Up to like & getrecommendations! Published in 2024 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.10158
Abstract: In this paper, we consider a nonlinear Schrödinger system with quadratic interaction. We extend the recent results of Fukaya et al. (Math. Ann. 2024) and show that the system has a ground state in ℝ4$$… read more here.
Keywords: system; system quadratic; schr dinger; quadratic interaction ... See more keywords
Quadratic Interaction Estimate for Hyperbolic Conservation Laws: an Overview
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Mathematical Sciences"
DOI: 10.1007/s10958-018-3972-0
Abstract: In a joint work with S. Bianchini [8] (see also [6, 7]), we proved a quadratic interaction estimate for the system of conservation lawsut+fux=0,ut=0=u0x,$$ \left\{\begin{array}{l}{u}_t+f{(u)}_x=0,\\ {}u\left(t=0\right)={u}_0(x),\end{array}\right. $$where u : [0, ∞) × ℝ → ℝn,… read more here.
Keywords: quadratic interaction; left alpha; alpha prime; interaction ... See more keywords
Dynamics of solutions of a fractional NLS system with quadratic interaction
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Mathematical Physics"
DOI: 10.1063/5.0045980
Abstract: The purpose of this article is twofold. First, we study the existence and asymptotic behavior of ground states of a fractional Schrodinger system with quadratic interaction. Second, we give some conditions, in terms of the… read more here.
Keywords: system quadratic; quadratic interaction; ground states; dynamics solutions ... See more keywords
Characterizing the postinflationary reheating history: Single daughter field with quadratic-quadratic interaction
Sign Up to like & getrecommendations! Published in 2022 at "Physical Review D"
DOI: 10.1103/physrevd.105.043532
Abstract: We study the evolution of the energy distribution and equation of state of the Universe from the end of inflation until the onset of either radiation domination (RD) or a transient period of matter domination… read more here.
Keywords: field quadratic; field; daughter field; quadratic quadratic ... See more keywords