-
Previous Article
Stability of variational eigenvalues for the fractional $p-$Laplacian
- DCDS Home
- This Issue
-
Next Article
Sharp estimates for fully bubbling solutions of $B_2$ Toda system
Stability of normalized solitary waves for three coupled nonlinear Schrödinger equations
1. | Trocaire College, Mathematics Department, 360 Choate Ave, Buffalo, NY 14220, United States |
References:
[1] |
J. Albert and J. Angulo, Existence and stability of ground-state solutions of a Schrödinger-KdV system, Proc. Royal Soc. of Edinburgh A, 133 (2003), 987-1029.
doi: 10.1017/S030821050000278X. |
[2] |
J. Albert and S. Bhattarai, Existence and stability of a two-parameter family of solitary waves for an NLS-KdV system, Adv. Differential Eqns., 18 (2013), 1129-1164. |
[3] |
J. Albert, J. Bona and J.-C. Saut, Model equations for waves in stratified fluids, Proc. Royal. Soc. of Edinburgh, Sect. A 453 (1997), 1233-1260.
doi: 10.1098/rspa.1997.0068. |
[4] |
T. B. Benjamin, The stability of solitary waves, Proc. Roy. Soc. London Ser. A, 328 (1972), 153-183.
doi: 10.1098/rspa.1972.0074. |
[5] |
S. Bhattarai, Solitary waves and a stability analysis for an equation of short and long dispersive waves, Nonlinear Anal., 75 (2012), 6506-6519.
doi: 10.1016/j.na.2012.07.026. |
[6] |
S. Bhattarai, Stability of solitary-wave solutions of coupled NLS equations with power-type nonlinearities, Adv. Nonlinear Anal., 4 (2015), 73-90.
doi: 10.1515/anona-2014-0058. |
[7] |
J. Bona, On the stability theory of solitary waves, Proc. Roy. Soc. London Ser. A, 344 (1975), 363-374.
doi: 10.1098/rspa.1975.0106. |
[8] |
J. Byeon, Effect of symmetry to the structure of positive solutions in nonlinear elliptic problems, J. Differential Eqns., 163 (2000), 429-474.
doi: 10.1006/jdeq.1999.3737. |
[9] |
T. Cazenave, Semilinear Schrödinger Equations, 10, AMS-Courant Lect. Notes in Math., 2003. |
[10] |
T. Cazenave and P. L. Lions, Orbital stability of standing waves for some nonlinear Schrödinger equations, Comm. Math. Phys., 85 (1982), 549-561.
doi: 10.1007/BF01403504. |
[11] |
S. Chakravarty, M. J. Ablowitz, J. R. Sauer and R. B. Jenkins, Multisoliton interactions and wavelength-division multiplexing, Opt. Lett., 20 (1995), 136-138.
doi: 10.1364/OL.20.000136. |
[12] |
F. Dalfovo, S. Giorgini, L. P. Pitaevskii and S. Stringari, Theory of Bose-Einstein condensation in trapped gases, Rev. Mod. Phys., 71 (1999), 463-512.
doi: 10.1103/RevModPhys.71.463. |
[13] |
T.-L. Ho, Spinor Bose condensates in optical traps, Phys. Rev. Lett., 81 (1998), p742.
doi: 10.1103/PhysRevLett.81.742. |
[14] |
Y. Kawaguchi and M. Ueda, Spinor Bose-Einstein condensates, Phys. Reports, 520 (2012), 253-381.
doi: 10.1016/j.physrep.2012.07.005. |
[15] |
E. H. Lieb and M. Loss, Analysis, 2nd ed., 14, AMS-Grad. Stud. Math., 2001.
doi: 10.1090/gsm/014. |
[16] |
P. L. Lions, The concentration-compactness principle in the calculus of variations. The locally compact case, Part 1, Ann. Inst. H. Poincaré Anal. Non Linéaire, 1 (1984), 109-145. |
[17] |
L. F. Mollenauer, S. G. Evangelides and J. P. Gordon, Wavelength division multiplexing with solitons in ultra-long transmission using lumped amplifiers, J. Lightwave Technol., 9 (1991), 362-367.
doi: 10.1109/50.70013. |
[18] |
N. V. Nguyen, R.-S. Tian, B. Deconinck and N. Sheils, Global existence for a system of Schrödinger equations with power-type nonlinearities, Jour. Math. Phys., 54 (2013), 011503.
doi: 10.1063/1.4774149. |
[19] |
N. V. Nguyen and Z-Q. Wang, Orbital stability of solitary waves for a nonlinear Schrodinger system, Adv. Differential Eqns., 16 (2011), 977-1000. |
[20] |
N. V. Nguyen and Z-Q. Wang, Orbital stability of solitary waves of a 3-coupled nonlinear Schrödinger system, Nonlinear Anal., 90 (2013), 1-26.
doi: 10.1016/j.na.2013.05.027. |
[21] |
N. V. Nguyen and Z-Q. Wang, Existence and stability of a two-parameter family of solitary waves for a 2-coupled nonlinear Schrödinger system, Discrete and Continuous Dynamical Systems - Series A (DCDS-A), 36 (2016), 1005-1021.
doi: 10.3934/dcds.2016.36.1005. |
[22] |
N. V. Nguyen, R. Tian and Z.-Q. Wang, Stability of traveling-wave solutions for a Schrödinger system with power-type nonlinearities,, preprint., ().
|
[23] |
M. Ohta, Stability of solitary waves for coupled nonlinear Schrödinger equations, Nonlinear Anal., 26 (1996), 933-939.
doi: 10.1016/0362-546X(94)00340-8. |
[24] |
A. C. Scott, Launching a davydov soliton: I. soliton analysis, Phys. Scr., 29 (1984), p279.
doi: 10.1088/0031-8949/29/3/016. |
[25] |
B. K. Som, M. R. Gupta and B. Dasgupta, Coupled nonlinear Schrödinger equation for Langmuir and dispersive ion acoustic waves, Phys. Lett. A, 72 (1979), 111-114.
doi: 10.1016/0375-9601(79)90663-7. |
[26] |
J. Q. Sun, Z. Q. Ma and M. Z. Qin, Simulation of envelope Rossby solitons in a pair of cubic Schrödinger equations, Appl. Math. Comput., 183 (2006), 946-952.
doi: 10.1016/j.amc.2006.06.041. |
[27] |
T. Tao, Nonlinear Dispersive Equations: Local and Global Analysis, 106 AMS-CBMS, 2006. |
[28] |
C. Yeh and L. Bergman, Enhanced pulse compression in a nonlinear fiber by a wavelength division multiplexed optical pulse, Phys. Rev. E, 57 (1998), p2398.
doi: 10.1103/PhysRevE.57.2398. |
show all references
References:
[1] |
J. Albert and J. Angulo, Existence and stability of ground-state solutions of a Schrödinger-KdV system, Proc. Royal Soc. of Edinburgh A, 133 (2003), 987-1029.
doi: 10.1017/S030821050000278X. |
[2] |
J. Albert and S. Bhattarai, Existence and stability of a two-parameter family of solitary waves for an NLS-KdV system, Adv. Differential Eqns., 18 (2013), 1129-1164. |
[3] |
J. Albert, J. Bona and J.-C. Saut, Model equations for waves in stratified fluids, Proc. Royal. Soc. of Edinburgh, Sect. A 453 (1997), 1233-1260.
doi: 10.1098/rspa.1997.0068. |
[4] |
T. B. Benjamin, The stability of solitary waves, Proc. Roy. Soc. London Ser. A, 328 (1972), 153-183.
doi: 10.1098/rspa.1972.0074. |
[5] |
S. Bhattarai, Solitary waves and a stability analysis for an equation of short and long dispersive waves, Nonlinear Anal., 75 (2012), 6506-6519.
doi: 10.1016/j.na.2012.07.026. |
[6] |
S. Bhattarai, Stability of solitary-wave solutions of coupled NLS equations with power-type nonlinearities, Adv. Nonlinear Anal., 4 (2015), 73-90.
doi: 10.1515/anona-2014-0058. |
[7] |
J. Bona, On the stability theory of solitary waves, Proc. Roy. Soc. London Ser. A, 344 (1975), 363-374.
doi: 10.1098/rspa.1975.0106. |
[8] |
J. Byeon, Effect of symmetry to the structure of positive solutions in nonlinear elliptic problems, J. Differential Eqns., 163 (2000), 429-474.
doi: 10.1006/jdeq.1999.3737. |
[9] |
T. Cazenave, Semilinear Schrödinger Equations, 10, AMS-Courant Lect. Notes in Math., 2003. |
[10] |
T. Cazenave and P. L. Lions, Orbital stability of standing waves for some nonlinear Schrödinger equations, Comm. Math. Phys., 85 (1982), 549-561.
doi: 10.1007/BF01403504. |
[11] |
S. Chakravarty, M. J. Ablowitz, J. R. Sauer and R. B. Jenkins, Multisoliton interactions and wavelength-division multiplexing, Opt. Lett., 20 (1995), 136-138.
doi: 10.1364/OL.20.000136. |
[12] |
F. Dalfovo, S. Giorgini, L. P. Pitaevskii and S. Stringari, Theory of Bose-Einstein condensation in trapped gases, Rev. Mod. Phys., 71 (1999), 463-512.
doi: 10.1103/RevModPhys.71.463. |
[13] |
T.-L. Ho, Spinor Bose condensates in optical traps, Phys. Rev. Lett., 81 (1998), p742.
doi: 10.1103/PhysRevLett.81.742. |
[14] |
Y. Kawaguchi and M. Ueda, Spinor Bose-Einstein condensates, Phys. Reports, 520 (2012), 253-381.
doi: 10.1016/j.physrep.2012.07.005. |
[15] |
E. H. Lieb and M. Loss, Analysis, 2nd ed., 14, AMS-Grad. Stud. Math., 2001.
doi: 10.1090/gsm/014. |
[16] |
P. L. Lions, The concentration-compactness principle in the calculus of variations. The locally compact case, Part 1, Ann. Inst. H. Poincaré Anal. Non Linéaire, 1 (1984), 109-145. |
[17] |
L. F. Mollenauer, S. G. Evangelides and J. P. Gordon, Wavelength division multiplexing with solitons in ultra-long transmission using lumped amplifiers, J. Lightwave Technol., 9 (1991), 362-367.
doi: 10.1109/50.70013. |
[18] |
N. V. Nguyen, R.-S. Tian, B. Deconinck and N. Sheils, Global existence for a system of Schrödinger equations with power-type nonlinearities, Jour. Math. Phys., 54 (2013), 011503.
doi: 10.1063/1.4774149. |
[19] |
N. V. Nguyen and Z-Q. Wang, Orbital stability of solitary waves for a nonlinear Schrodinger system, Adv. Differential Eqns., 16 (2011), 977-1000. |
[20] |
N. V. Nguyen and Z-Q. Wang, Orbital stability of solitary waves of a 3-coupled nonlinear Schrödinger system, Nonlinear Anal., 90 (2013), 1-26.
doi: 10.1016/j.na.2013.05.027. |
[21] |
N. V. Nguyen and Z-Q. Wang, Existence and stability of a two-parameter family of solitary waves for a 2-coupled nonlinear Schrödinger system, Discrete and Continuous Dynamical Systems - Series A (DCDS-A), 36 (2016), 1005-1021.
doi: 10.3934/dcds.2016.36.1005. |
[22] |
N. V. Nguyen, R. Tian and Z.-Q. Wang, Stability of traveling-wave solutions for a Schrödinger system with power-type nonlinearities,, preprint., ().
|
[23] |
M. Ohta, Stability of solitary waves for coupled nonlinear Schrödinger equations, Nonlinear Anal., 26 (1996), 933-939.
doi: 10.1016/0362-546X(94)00340-8. |
[24] |
A. C. Scott, Launching a davydov soliton: I. soliton analysis, Phys. Scr., 29 (1984), p279.
doi: 10.1088/0031-8949/29/3/016. |
[25] |
B. K. Som, M. R. Gupta and B. Dasgupta, Coupled nonlinear Schrödinger equation for Langmuir and dispersive ion acoustic waves, Phys. Lett. A, 72 (1979), 111-114.
doi: 10.1016/0375-9601(79)90663-7. |
[26] |
J. Q. Sun, Z. Q. Ma and M. Z. Qin, Simulation of envelope Rossby solitons in a pair of cubic Schrödinger equations, Appl. Math. Comput., 183 (2006), 946-952.
doi: 10.1016/j.amc.2006.06.041. |
[27] |
T. Tao, Nonlinear Dispersive Equations: Local and Global Analysis, 106 AMS-CBMS, 2006. |
[28] |
C. Yeh and L. Bergman, Enhanced pulse compression in a nonlinear fiber by a wavelength division multiplexed optical pulse, Phys. Rev. E, 57 (1998), p2398.
doi: 10.1103/PhysRevE.57.2398. |
[1] |
Nghiem V. Nguyen, Zhi-Qiang Wang. Existence and stability of a two-parameter family of solitary waves for a 2-coupled nonlinear Schrödinger system. Discrete and Continuous Dynamical Systems, 2016, 36 (2) : 1005-1021. doi: 10.3934/dcds.2016.36.1005 |
[2] |
Benedetta Noris, Hugo Tavares, Gianmaria Verzini. Stable solitary waves with prescribed $L^2$-mass for the cubic Schrödinger system with trapping potentials. Discrete and Continuous Dynamical Systems, 2015, 35 (12) : 6085-6112. doi: 10.3934/dcds.2015.35.6085 |
[3] |
Zhanping Liang, Yuanmin Song, Fuyi Li. Positive ground state solutions of a quadratically coupled schrödinger system. Communications on Pure and Applied Analysis, 2017, 16 (3) : 999-1012. doi: 10.3934/cpaa.2017048 |
[4] |
Scipio Cuccagna, Masaya Maeda. A survey on asymptotic stability of ground states of nonlinear Schrödinger equations II. Discrete and Continuous Dynamical Systems - S, 2021, 14 (5) : 1693-1716. doi: 10.3934/dcdss.2020450 |
[5] |
Andrew Comech, Scipio Cuccagna. On asymptotic stability of ground states of some systems of nonlinear Schrödinger equations. Discrete and Continuous Dynamical Systems, 2021, 41 (3) : 1225-1270. doi: 10.3934/dcds.2020316 |
[6] |
Chuangye Liu, Zhi-Qiang Wang. A complete classification of ground-states for a coupled nonlinear Schrödinger system. Communications on Pure and Applied Analysis, 2017, 16 (1) : 115-130. doi: 10.3934/cpaa.2017005 |
[7] |
Alex H. Ardila, Mykael Cardoso. Blow-up solutions and strong instability of ground states for the inhomogeneous nonlinear Schrödinger equation. Communications on Pure and Applied Analysis, 2021, 20 (1) : 101-119. doi: 10.3934/cpaa.2020259 |
[8] |
Chuangye Liu, Rushun Tian. Normalized solutions for 3-coupled nonlinear Schrödinger equations. Communications on Pure and Applied Analysis, 2020, 19 (11) : 5115-5130. doi: 10.3934/cpaa.2020229 |
[9] |
Songbai Peng, Aliang Xia. Normalized solutions of supercritical nonlinear fractional Schrödinger equation with potential. Communications on Pure and Applied Analysis, 2021, 20 (11) : 3723-3744. doi: 10.3934/cpaa.2021128 |
[10] |
Haidong Liu, Zhaoli Liu. Positive solutions of a nonlinear Schrödinger system with nonconstant potentials. Discrete and Continuous Dynamical Systems, 2016, 36 (3) : 1431-1464. doi: 10.3934/dcds.2016.36.1431 |
[11] |
Chunhua Wang, Jing Yang. Positive solutions for a nonlinear Schrödinger-Poisson system. Discrete and Continuous Dynamical Systems, 2018, 38 (11) : 5461-5504. doi: 10.3934/dcds.2018241 |
[12] |
Chunhua Li. Decay of solutions for a system of nonlinear Schrödinger equations in 2D. Discrete and Continuous Dynamical Systems, 2012, 32 (12) : 4265-4285. doi: 10.3934/dcds.2012.32.4265 |
[13] |
Yong Luo, Shu Zhang. Concentration behavior of ground states for $ L^2 $-critical Schrödinger Equation with a spatially decaying nonlinearity. Communications on Pure and Applied Analysis, 2022, 21 (4) : 1481-1504. doi: 10.3934/cpaa.2022026 |
[14] |
Mohammad Ali Husaini, Chuangye Liu. Synchronized and ground-state solutions to a coupled Schrödinger system. Communications on Pure and Applied Analysis, 2022, 21 (2) : 639-667. doi: 10.3934/cpaa.2021192 |
[15] |
Alex H. Ardila. Stability of ground states for logarithmic Schrödinger equation with a $δ^{\prime}$-interaction. Evolution Equations and Control Theory, 2017, 6 (2) : 155-175. doi: 10.3934/eect.2017009 |
[16] |
Sevdzhan Hakkaev. Orbital stability of solitary waves of the Schrödinger-Boussinesq equation. Communications on Pure and Applied Analysis, 2007, 6 (4) : 1043-1050. doi: 10.3934/cpaa.2007.6.1043 |
[17] |
Zupei Shen, Zhiqing Han, Qinqin Zhang. Ground states of nonlinear Schrödinger equations with fractional Laplacians. Discrete and Continuous Dynamical Systems - S, 2019, 12 (7) : 2115-2125. doi: 10.3934/dcdss.2019136 |
[18] |
Patricio Felmer, César Torres. Radial symmetry of ground states for a regional fractional Nonlinear Schrödinger Equation. Communications on Pure and Applied Analysis, 2014, 13 (6) : 2395-2406. doi: 10.3934/cpaa.2014.13.2395 |
[19] |
Rong Cheng, Jun Wang. Existence of ground states for Schrödinger-Poisson system with nonperiodic potentials. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2021317 |
[20] |
Juan Belmonte-Beitia, Vladyslav Prytula. Existence of solitary waves in nonlinear equations of Schrödinger type. Discrete and Continuous Dynamical Systems - S, 2011, 4 (5) : 1007-1017. doi: 10.3934/dcdss.2011.4.1007 |
2020 Impact Factor: 1.392
Tools
Metrics
Other articles
by authors
[Back to Top]