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

doi:10.1007/s10473-020-0214-6

Abstract

CLC Number:

35Q44

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.

Trendmd

[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

[1]	Hua CHEN, Huiyang XU. GLOBAL EXISTENCE, EXPONENTIAL DECAY AND BLOW-UP IN FINITE TIME FOR A CLASS OF FINITELY DEGENERATE SEMILINEAR PARABOLIC EQUATIONS [J]. Acta mathematica scientia,Series B, 2019, 39(5): 1290-1308.
[2]	Ying WANG, Mingxin WANG. BOUNDARY BLOW-UP RATE OF THE LARGE SOLUTION FOR AN ELLIPTIC COOPERATIVE SYSTEM [J]. Acta mathematica scientia,Series B, 2019, 39(5): 1363-1379.
[3]	Ya WANG, Yu-Xia LIANG. DISJOINT SUPERCYCLIC WEIGHTED PSEUDO-SHIFTS ON BANACH SEQUENCE SPACES [J]. Acta mathematica scientia,Series B, 2019, 39(4): 1089-1102.
[4]	Jae-Myoung KIM. LOCAL EXISTENCE AND BLOW-UP CRITERION OF 3D IDEAL MAGNETOHYDRODYNAMICS EQUATIONS [J]. Acta mathematica scientia,Series B, 2018, 38(6): 1759-1766.
[5]	Yue-Loong CHANG, Meng-Rong LI, C. Jack YUE, Yong-Shiuan LEE, Tsung-Jui CHIANG-LIN. MATHEMATICAL MODEL FOR THE ENTERPRISE COMPETITIVE ABILITY AND PERFORMANCE THROUGH A PARTICULAR EMDEN-FOWLER EQUATION u"-n^-q-1u (n)^q=0 [J]. Acta mathematica scientia,Series B, 2018, 38(4): 1311-1321.
[6]	Yong LIN, Yiting WU. BLOW-UP PROBLEMS FOR NONLINEAR PARABOLIC EQUATIONS ON LOCALLY FINITE GRAPHS [J]. Acta mathematica scientia,Series B, 2018, 38(3): 843-856.
[7]	Xincai ZHU. EXISTENCE AND BLOW-UP BEHAVIOR OF CONSTRAINED MINIMIZERS FOR SCHRÖDINGER-POISSON-SLATER SYSTEM [J]. Acta mathematica scientia,Series B, 2018, 38(2): 733-744.
[8]	Lingyan YANG, Xiaoguang LI, Yonghong WU, Louis CACCETTA. GLOBAL WELL-POSEDNESS AND BLOW-UP FOR THE HARTREE EQUATION [J]. Acta mathematica scientia,Series B, 2017, 37(4): 941-948.
[9]	Huihui KONG, Hai-Liang LI, Xingwei ZHANG. A BLOW-UP CRITERION OF SPHERICALLY SYMMETRIC STRONG SOLUTIONS TO 3D COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH FREE BOUNDARY [J]. Acta mathematica scientia,Series B, 2016, 36(4): 1153-1166.
[10]	Shengguo ZHU. BLOW-UP OF CLASSICAL SOLUTIONS TO THE COMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS WITH VACUUM [J]. Acta mathematica scientia,Series B, 2016, 36(1): 220-232.
[11]	Pan ZHENG, Chunlai MU, Xuegang HU, Fuchen ZHANG. SECONDARY CRITICAL EXPONENT AND LIFE SPAN FOR A DOUBLY SINGULAR PARABOLIC EQUATION WITH A WEIGHTED SOURCE [J]. Acta mathematica scientia,Series B, 2016, 36(1): 244-256.
[12]	Ran DUAN, Fei JIANG, Fei JIANG. RAYLEIGH-TAYLOR INSTABILITY FOR COMPRESSIBLE ROTATING FLOWS [J]. Acta mathematica scientia,Series B, 2015, 35(6): 1359-1385.
[13]	Yueloong CHANG, Mengrong LI. A MATHEMATICAL MODEL OF ENTERPRISE COMPETITIVE ABILITY AND PERFORMANCE THROUGH EMDEN-FOWLER EQUATION FOR SOME ENTERPRISES [J]. Acta mathematica scientia,Series B, 2015, 35(5): 1014-1022.
[14]	Zaihui GAN, Boling GUO, Xin JIANG. ORBITAL INSTABILITY OF STANDING WAVES FOR THE GENERALIZED 3D NONLOCAL NONLINEAR SCHRÖDINGER EQUATIONS [J]. Acta mathematica scientia,Series B, 2015, 35(5): 1163-1188.
[15]	LI Yu-Huan, MI Yong-Sheng, MU Chun-Lai. PROPERTIES OF POSITIVE SOLUTIONS FOR A NONLOCAL NONLINEAR DIFFUSION EQUATION WITH NONLOCAL NONLINEAR BOUNDARY CONDITION [J]. Acta mathematica scientia,Series B, 2014, 34(3): 748-758.

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

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 0