Articles

STRONG INSTABILITY OF STANDING WAVES FOR A SYSTEM NLS WITH QUADRATIC INTERACTION

  • Van Duong DINH
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  • 1. Laboratoire Paul Painlevé UMR 8524, Université de Lille CNRS, 59655 Villeneuve d'Ascq, Cedex, France;
    2. Department of Mathematics, HCMC University of Pedagogy, 280 An Duong Vuong, Ho Chi Minh, Vietnam

Received date: 2018-12-28

  Online published: 2020-05-26

Supported by

The author is supported by the Labex CEMPI (ANR-11-LABX-0007-01).

Abstract

We study the strong instability of standing waves for a system of nonlinear Schrödinger equations with quadratic interaction under the mass resonance condition in dimension d=5.

Cite this article

Van Duong DINH . STRONG INSTABILITY OF STANDING WAVES FOR A SYSTEM NLS WITH QUADRATIC INTERACTION[J]. Acta mathematica scientia, Series B, 2020 , 40(2) : 515 -528 . DOI: 10.1007/s10473-020-0214-6

References

[1] Cazenave T. Semilinear Schrödinger Equations, Courant Lecture Notes in Mathematics, 10. Courant Institute of Mathematical Sciences:American Mathematical Society, 2003
[2] Colin M, Colin T, Ohta M. Instability of standing waves for a system of nonlinear Schrödinger equations with three-wave interaction. Funkcial Ekvac, 2009, 52:371-380
[3] Colin M, Di Menza L, Saut J C. Solitons in quadratic media. Nonlinearity, 2016, 29:1000-1035
[4] Dinh V D. Existence, stability of standing waves and the characterization of finite time blow-up solutions for a system NLS with quadratic interaction. Nonlinear Anal, 2020, 190:111589
[5] Glassey R T. On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations. J Math Phys, 1977, 18:1794-1797
[6] Hamano M. Global dynamics below the ground state for the quadratic Schrödinger system in 5D. Preprint arXiv:1805.12245, 2018
[7] Hoshino G, Ozawa T. Analytic smoothing effect for a system of nonlinear Schrödinger equations. Differ Equ Appl, 2013, 5:395-408
[8] Hoshino G, Ozawa T. Analytic smoothing effect for a system of Schrödinger equations with two wave interaction. Adv Differential Equations, 2015, 20:697-716
[9] Hoshino G. Space-time analytic smoothing effect for global solutions to a system of nonlinear Schrödinger equations with large data. Ann Henri Poincaré, 2018, 19:2101-2114
[10] Hayashi N, Li C, Naumkin P I. On a system of nonlinear Schrödinger equation in 2D. Differential Integral Equations, 2011, 24:417-434
[11] Hayashi N, Li C, Naumkin P I. Modified wave operator for a system of nonlinear Schrödinger equations in 2D. Commun Partial Differential Equations, 2012, 37:947-968
[12] Hayashi N, Li C, Ozawa T. Small data scattering for a system of nonlinear Schrödinger equations. Differ Equ Appl, 2011, 3:415-426
[13] Hayashi N, Ozawa T, Tanaka K. On a system of nonlinear Schrödinger equations with quadratic interaction. Ann Inst H Poincaré Anal Non Linéaire, 2013, 30:661-690
[14] Ogawa T, Uriya K. Final state problem for a quadratic nonlinear Schrödinger system in two space dimensions with mass resonance. J Differential Equations, 2015, 258:483-583
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