2006, 6(1): 203-214. doi: 10.3934/dcdsb.2006.6.203

Cauchy problem for the nonlinear Schrödinger-IMBq equations

1. 

Department of Mathematics, Zhengzhou University, Zhengzhou 450052, China, China

Received  November 2004 Revised  July 2005 Published  October 2005

In this paper, the existence and uniqueness of the global strong solution of the Cauchy problem for nonlinear Schrödinger-IMBq equations are proved.
Citation: Shubin Wang, Guowang Chen. Cauchy problem for the nonlinear Schrödinger-IMBq equations. Discrete & Continuous Dynamical Systems - B, 2006, 6 (1) : 203-214. doi: 10.3934/dcdsb.2006.6.203
[1]

Paolo Antonelli, Daniel Marahrens, Christof Sparber. On the Cauchy problem for nonlinear Schrödinger equations with rotation. Discrete & Continuous Dynamical Systems - A, 2012, 32 (3) : 703-715. doi: 10.3934/dcds.2012.32.703

[2]

Changxing Miao, Bo Zhang. Global well-posedness of the Cauchy problem for nonlinear Schrödinger-type equations. Discrete & Continuous Dynamical Systems - A, 2007, 17 (1) : 181-200. doi: 10.3934/dcds.2007.17.181

[3]

Binhua Feng, Xiangxia Yuan. On the Cauchy problem for the Schrödinger-Hartree equation. Evolution Equations & Control Theory, 2015, 4 (4) : 431-445. doi: 10.3934/eect.2015.4.431

[4]

Binhua Feng, Dun Zhao. On the Cauchy problem for the XFEL Schrödinger equation. Discrete & Continuous Dynamical Systems - B, 2017, 22 (11) : 1-16. doi: 10.3934/dcdsb.2018131

[5]

Jianqing Chen, Boling Guo. Sharp global existence and blowing up results for inhomogeneous Schrödinger equations. Discrete & Continuous Dynamical Systems - B, 2007, 8 (2) : 357-367. doi: 10.3934/dcdsb.2007.8.357

[6]

Rémi Carles. Global existence results for nonlinear Schrödinger equations with quadratic potentials. Discrete & Continuous Dynamical Systems - A, 2005, 13 (2) : 385-398. doi: 10.3934/dcds.2005.13.385

[7]

Zaihui Gan, Boling Guo, Jian Zhang. Blowup and global existence of the nonlinear Schrödinger equations with multiple potentials. Communications on Pure & Applied Analysis, 2009, 8 (4) : 1303-1312. doi: 10.3934/cpaa.2009.8.1303

[8]

Masahoto Ohta, Grozdena Todorova. Remarks on global existence and blowup for damped nonlinear Schrödinger equations. Discrete & Continuous Dynamical Systems - A, 2009, 23 (4) : 1313-1325. doi: 10.3934/dcds.2009.23.1313

[9]

Chunxiao Guo, Fan Cui, Yongqian Han. Global existence and uniqueness of the solution for the fractional Schrödinger-KdV-Burgers system. Discrete & Continuous Dynamical Systems - S, 2016, 9 (6) : 1687-1699. doi: 10.3934/dcdss.2016070

[10]

Yang Han. On the cauchy problem for the coupled Klein Gordon Schrödinger system with rough data. Discrete & Continuous Dynamical Systems - A, 2005, 12 (2) : 233-242. doi: 10.3934/dcds.2005.12.233

[11]

Li Liang. Increasing stability for the inverse problem of the Schrödinger equation with the partial Cauchy data. Inverse Problems & Imaging, 2015, 9 (2) : 469-478. doi: 10.3934/ipi.2015.9.469

[12]

Hiroyuki Hirayama, Mamoru Okamoto. Random data Cauchy problem for the nonlinear Schrödinger equation with derivative nonlinearity. Discrete & Continuous Dynamical Systems - A, 2016, 36 (12) : 6943-6974. doi: 10.3934/dcds.2016102

[13]

Carlos Kenig, Tobias Lamm, Daniel Pollack, Gigliola Staffilani, Tatiana Toro. The Cauchy problem for Schrödinger flows into Kähler manifolds. Discrete & Continuous Dynamical Systems - A, 2010, 27 (2) : 389-439. doi: 10.3934/dcds.2010.27.389

[14]

GUANGBING LI. Positive solution for quasilinear Schrödinger equations with a parameter. Communications on Pure & Applied Analysis, 2015, 14 (5) : 1803-1816. doi: 10.3934/cpaa.2015.14.1803

[15]

Fouad Hadj Selem, Hiroaki Kikuchi, Juncheng Wei. Existence and uniqueness of singular solution to stationary Schrödinger equation with supercritical nonlinearity. Discrete & Continuous Dynamical Systems - A, 2013, 33 (10) : 4613-4626. doi: 10.3934/dcds.2013.33.4613

[16]

J. Colliander, Justin Holmer, Monica Visan, Xiaoyi Zhang. Global existence and scattering for rough solutions to generalized nonlinear Schrödinger equations on $R$. Communications on Pure & Applied Analysis, 2008, 7 (3) : 467-489. doi: 10.3934/cpaa.2008.7.467

[17]

Tadahiro Oh. Global existence for the defocusing nonlinear Schrödinger equations with limit periodic initial data. Communications on Pure & Applied Analysis, 2015, 14 (4) : 1563-1580. doi: 10.3934/cpaa.2015.14.1563

[18]

Zaihui Gan, Jian Zhang. Blow-up, global existence and standing waves for the magnetic nonlinear Schrödinger equations. Discrete & Continuous Dynamical Systems - A, 2012, 32 (3) : 827-846. doi: 10.3934/dcds.2012.32.827

[19]

Jason Murphy, Fabio Pusateri. Almost global existence for cubic nonlinear Schrödinger equations in one space dimension. Discrete & Continuous Dynamical Systems - A, 2017, 37 (4) : 2077-2102. doi: 10.3934/dcds.2017089

[20]

Takashi Narazaki. Global solutions to the Cauchy problem for the weakly coupled system of damped wave equations. Conference Publications, 2009, 2009 (Special) : 592-601. doi: 10.3934/proc.2009.2009.592

2016 Impact Factor: 0.994

Metrics

  • PDF downloads (1)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]