-
Previous Article
Global well-posedness for the 3D Zakharov-Kuznetsov equation in energy space $H^1$
- DCDS-S Home
- This Issue
-
Next Article
Global smooth solutions for the nonlinear Schrödinger equation with magnetic effect
Periodic solutions of inhomogeneous Schrödinger flows into 2-sphere
1. | Department of Mathematics, Shanghai University, Shanghai 200444, China |
2. | Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100190, China |
References:
[1] |
W. Chen and J. Jost, Maps with prescribed tension fields,, Comm. Anal. Geom., 12 (2004), 93.
doi: 10.4310/CAG.2004.v12.n1.a6. |
[2] |
N. Chang, J. Shatah and K. Uhlenbeck, Schrödinger maps,, Comm. Pure Appl. Math., 53 (2000), 590.
doi: 10.1002/(SICI)1097-0312(200005)53:5<590::AID-CPA2>3.0.CO;2-R. |
[3] |
Q. Ding, A note on NLS and the Schödinger flow of maps,, Phys. Lett. A, 248 (1998), 49. Google Scholar |
[4] |
W. Ding, Lusternik-Schnirelmann theory for harmonic maps,, Acta Math. Sinica (N. S.), 2 (1986), 105.
doi: 10.1007/BF02564873. |
[5] |
W. Y. Ding and Y. D. Wang, Schrödinger flow of mappings into sympletic manifolds,, Sci. China Ser. A, 41 (1998), 746.
doi: 10.1007/BF02901957. |
[6] |
W. Y. Ding and Y. D. Wang, Local Schrödinger flow into Kähler manifolds,, Sci. China Ser. A, 44 (2001), 1446.
doi: 10.1007/BF02877074. |
[7] |
W. Y. Ding and H. Yin, Special periodic Solutions of Schrödinger flow,, Math. Z., 253 (2006), 555.
doi: 10.1007/s00209-005-0922-6. |
[8] |
J. Eells and L. Lemaire, Another report on harmonic maps,, London Math Soc., 20 (1988), 385.
doi: 10.1112/blms/20.5.385. |
[9] |
S. Gustafson and J. Shatah, The stability of localize solutions of Landau-Lifshitz equations,, J. Comm. Pure Appl. Math., 55 (2002), 1136.
doi: 10.1002/cpa.3024. |
[10] |
P. L. Huang, On some inhomogeneous Geometirc PDEs,, Ph.D thesis, (2007). Google Scholar |
[11] |
Y. X. Li and Y. D. Wang, Bubbling location for f-harmonic maps and inhomogeneous Landau-Lifshitz equations,, Comm. Math. Helv., 81 (2006), 433.
|
[12] |
S. Kobayashi, Transformation Groups in Differential Geometry,, Springer-Verlag, (1972).
|
[13] |
A. M. Kosevich, B. A. Ivanov and A. S. Kovalev, Magnetic solitons,, Phys. Rep., 194 (1990), 117.
doi: 10.1016/0370-1573(90)90130-T. |
[14] |
R. S. Palais, The principle of symmetric criticality,, Comm. Math. Phys., 69 (1979), 19.
doi: 10.1007/BF01941322. |
[15] |
P. Y. H. Pang, H. Wang and Y. D. Wang, Local existence for inhomogeneous Schrödinger flow into Kähler manifolds,, Acta Math. Sinica, 16 (2000), 487.
doi: 10.1007/s101140000060. |
[16] |
P. Y. H. Pang, H. Wang and Y. D. Wang, Schrödinger flow for maps into Kähler manifolds,, Asian J. Math., 5 (2001), 509.
doi: 10.4310/AJM.2001.v5.n3.a7. |
[17] |
P. Y. H. Pang, H. Wang and Y. D. Wang, Schrödinger flow on Hermitian locally symmetric spaces,, Comm. Anal. Geom., 10 (2002), 653.
doi: 10.4310/CAG.2002.v10.n4.a1. |
[18] |
X. Peng and G. Wang, Harmonic maps with a prescribed potential,, C. R. Acad. Sci., 327 (1998), 271.
doi: 10.1016/S0764-4442(98)80145-6. |
[19] |
B. Piette and W. J. Zakrzewski, Localized solutions in a two-dimensional Landau-Lifshitz model,, Physic D, 119 (1998), 314.
doi: 10.1016/S0167-2789(98)00084-0. |
[20] |
M. Struwe, Variational Methods,, $3^{rd}$ edition, (2000).
doi: 10.1007/978-3-662-04194-9. |
[21] |
P. Sulem, C. Sulem and C. Bardos, On the continuous limit for a system of classical spins,, Comm. Math. Phys., 107 (1986), 431.
doi: 10.1007/BF01220998. |
[22] |
J. Sacks and K. Uhlenbeck, The existence of minimal immersions of 2-spheres,, Ann. Math., 113 (1981), 1.
doi: 10.2307/1971131. |
[23] |
H. Wang and Y. D. Wang, Global existence of inhomogeneous Heisenberg spin systems and Schrödinger flow,, Internat. J. Math., 11 (2000), 1079.
doi: 10.1142/S0129167X00000568. |
[24] |
H. Yin, Periodic solutions of Schrödinger flow from $S^3$ to $S^2$,, Chinese Ann. Math. Ser. B, 27 (2006), 401.
doi: 10.1007/s11401-005-0101-4. |
[25] |
Y. Zhou, B. Guo and S. Tan, Existence and uniqueness of Smooth solution for system of ferromagnetic chain,, Science in China A, 34 (1991), 257.
|
show all references
References:
[1] |
W. Chen and J. Jost, Maps with prescribed tension fields,, Comm. Anal. Geom., 12 (2004), 93.
doi: 10.4310/CAG.2004.v12.n1.a6. |
[2] |
N. Chang, J. Shatah and K. Uhlenbeck, Schrödinger maps,, Comm. Pure Appl. Math., 53 (2000), 590.
doi: 10.1002/(SICI)1097-0312(200005)53:5<590::AID-CPA2>3.0.CO;2-R. |
[3] |
Q. Ding, A note on NLS and the Schödinger flow of maps,, Phys. Lett. A, 248 (1998), 49. Google Scholar |
[4] |
W. Ding, Lusternik-Schnirelmann theory for harmonic maps,, Acta Math. Sinica (N. S.), 2 (1986), 105.
doi: 10.1007/BF02564873. |
[5] |
W. Y. Ding and Y. D. Wang, Schrödinger flow of mappings into sympletic manifolds,, Sci. China Ser. A, 41 (1998), 746.
doi: 10.1007/BF02901957. |
[6] |
W. Y. Ding and Y. D. Wang, Local Schrödinger flow into Kähler manifolds,, Sci. China Ser. A, 44 (2001), 1446.
doi: 10.1007/BF02877074. |
[7] |
W. Y. Ding and H. Yin, Special periodic Solutions of Schrödinger flow,, Math. Z., 253 (2006), 555.
doi: 10.1007/s00209-005-0922-6. |
[8] |
J. Eells and L. Lemaire, Another report on harmonic maps,, London Math Soc., 20 (1988), 385.
doi: 10.1112/blms/20.5.385. |
[9] |
S. Gustafson and J. Shatah, The stability of localize solutions of Landau-Lifshitz equations,, J. Comm. Pure Appl. Math., 55 (2002), 1136.
doi: 10.1002/cpa.3024. |
[10] |
P. L. Huang, On some inhomogeneous Geometirc PDEs,, Ph.D thesis, (2007). Google Scholar |
[11] |
Y. X. Li and Y. D. Wang, Bubbling location for f-harmonic maps and inhomogeneous Landau-Lifshitz equations,, Comm. Math. Helv., 81 (2006), 433.
|
[12] |
S. Kobayashi, Transformation Groups in Differential Geometry,, Springer-Verlag, (1972).
|
[13] |
A. M. Kosevich, B. A. Ivanov and A. S. Kovalev, Magnetic solitons,, Phys. Rep., 194 (1990), 117.
doi: 10.1016/0370-1573(90)90130-T. |
[14] |
R. S. Palais, The principle of symmetric criticality,, Comm. Math. Phys., 69 (1979), 19.
doi: 10.1007/BF01941322. |
[15] |
P. Y. H. Pang, H. Wang and Y. D. Wang, Local existence for inhomogeneous Schrödinger flow into Kähler manifolds,, Acta Math. Sinica, 16 (2000), 487.
doi: 10.1007/s101140000060. |
[16] |
P. Y. H. Pang, H. Wang and Y. D. Wang, Schrödinger flow for maps into Kähler manifolds,, Asian J. Math., 5 (2001), 509.
doi: 10.4310/AJM.2001.v5.n3.a7. |
[17] |
P. Y. H. Pang, H. Wang and Y. D. Wang, Schrödinger flow on Hermitian locally symmetric spaces,, Comm. Anal. Geom., 10 (2002), 653.
doi: 10.4310/CAG.2002.v10.n4.a1. |
[18] |
X. Peng and G. Wang, Harmonic maps with a prescribed potential,, C. R. Acad. Sci., 327 (1998), 271.
doi: 10.1016/S0764-4442(98)80145-6. |
[19] |
B. Piette and W. J. Zakrzewski, Localized solutions in a two-dimensional Landau-Lifshitz model,, Physic D, 119 (1998), 314.
doi: 10.1016/S0167-2789(98)00084-0. |
[20] |
M. Struwe, Variational Methods,, $3^{rd}$ edition, (2000).
doi: 10.1007/978-3-662-04194-9. |
[21] |
P. Sulem, C. Sulem and C. Bardos, On the continuous limit for a system of classical spins,, Comm. Math. Phys., 107 (1986), 431.
doi: 10.1007/BF01220998. |
[22] |
J. Sacks and K. Uhlenbeck, The existence of minimal immersions of 2-spheres,, Ann. Math., 113 (1981), 1.
doi: 10.2307/1971131. |
[23] |
H. Wang and Y. D. Wang, Global existence of inhomogeneous Heisenberg spin systems and Schrödinger flow,, Internat. J. Math., 11 (2000), 1079.
doi: 10.1142/S0129167X00000568. |
[24] |
H. Yin, Periodic solutions of Schrödinger flow from $S^3$ to $S^2$,, Chinese Ann. Math. Ser. B, 27 (2006), 401.
doi: 10.1007/s11401-005-0101-4. |
[25] |
Y. Zhou, B. Guo and S. Tan, Existence and uniqueness of Smooth solution for system of ferromagnetic chain,, Science in China A, 34 (1991), 257.
|
[1] |
Jong-Shenq Guo, Ying-Chih Lin. Traveling wave solution for a lattice dynamical system with convolution type nonlinearity. Discrete & Continuous Dynamical Systems - A, 2012, 32 (1) : 101-124. doi: 10.3934/dcds.2012.32.101 |
[2] |
Patrizia Pucci. Critical Schrödinger-Hardy systems in the Heisenberg group. Discrete & Continuous Dynamical Systems - S, 2019, 12 (2) : 375-400. doi: 10.3934/dcdss.2019025 |
[3] |
Fábio Natali, Ademir Pastor. Orbital stability of periodic waves for the Klein-Gordon-Schrödinger system. Discrete & Continuous Dynamical Systems - A, 2011, 31 (1) : 221-238. doi: 10.3934/dcds.2011.31.221 |
[4] |
Daniela De Silva, Nataša Pavlović, Gigliola Staffilani, Nikolaos Tzirakis. Global well-posedness for a periodic nonlinear Schrödinger equation in 1D and 2D. Discrete & Continuous Dynamical Systems - A, 2007, 19 (1) : 37-65. doi: 10.3934/dcds.2007.19.37 |
[5] |
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 |
[6] |
Zhengping Wang, Huan-Song Zhou. Positive solution for a nonlinear stationary Schrödinger-Poisson system in $R^3$. Discrete & Continuous Dynamical Systems - A, 2007, 18 (4) : 809-816. doi: 10.3934/dcds.2007.18.809 |
[7] |
Pavel I. Naumkin, Isahi Sánchez-Suárez. On the critical nongauge invariant nonlinear Schrödinger equation. Discrete & Continuous Dynamical Systems - A, 2011, 30 (3) : 807-834. doi: 10.3934/dcds.2011.30.807 |
[8] |
Francois Ledrappier and Omri Sarig. Invariant measures for the horocycle flow on periodic hyperbolic surfaces. Electronic Research Announcements, 2005, 11: 89-94. |
[9] |
Chu-Hee Cho, Youngwoo Koh, Ihyeok Seo. On inhomogeneous Strichartz estimates for fractional Schrödinger equations and their applications. Discrete & Continuous Dynamical Systems - A, 2016, 36 (4) : 1905-1926. doi: 10.3934/dcds.2016.36.1905 |
[10] |
Yue Liu. Existence of unstable standing waves for the inhomogeneous nonlinear Schrödinger equation. Communications on Pure & Applied Analysis, 2008, 7 (1) : 193-209. doi: 10.3934/cpaa.2008.7.193 |
[11] |
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 |
[12] |
Valeria Banica, Luis Vega. Singularity formation for the 1-D cubic NLS and the Schrödinger map on $\mathbb S^2$. Communications on Pure & Applied Analysis, 2018, 17 (4) : 1317-1329. doi: 10.3934/cpaa.2018064 |
[13] |
Hiroko Morimoto. Survey on time periodic problem for fluid flow under inhomogeneous boundary condition. Discrete & Continuous Dynamical Systems - S, 2012, 5 (3) : 631-639. doi: 10.3934/dcdss.2012.5.631 |
[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] |
Fábio Natali, Ademir Pastor. Stability properties of periodic standing waves for the Klein-Gordon-Schrödinger system. Communications on Pure & Applied Analysis, 2010, 9 (2) : 413-430. doi: 10.3934/cpaa.2010.9.413 |
[16] |
Boling Guo, Haiyang Huang. Smooth solution of the generalized system of ferro-magnetic chain. Discrete & Continuous Dynamical Systems - A, 1999, 5 (4) : 729-740. doi: 10.3934/dcds.1999.5.729 |
[17] |
Alexander Arbieto, Carlos Matheus. On the periodic Schrödinger-Debye equation. Communications on Pure & Applied Analysis, 2008, 7 (3) : 699-713. doi: 10.3934/cpaa.2008.7.699 |
[18] |
Alexander Pankov. Nonlinear Schrödinger Equations on Periodic Metric Graphs. Discrete & Continuous Dynamical Systems - A, 2018, 38 (2) : 697-714. doi: 10.3934/dcds.2018030 |
[19] |
Jean Bourgain. On quasi-periodic lattice Schrödinger operators. Discrete & Continuous Dynamical Systems - A, 2004, 10 (1&2) : 75-88. doi: 10.3934/dcds.2004.10.75 |
[20] |
M. I. Alomar, David Sánchez. Thermopower of a graphene monolayer with inhomogeneous spin-orbit interaction. Conference Publications, 2015, 2015 (special) : 1-9. doi: 10.3934/proc.2015.0001 |
2018 Impact Factor: 0.545
Tools
Metrics
Other articles
by authors
[Back to Top]