Stability of normalized solitary waves for three coupled nonlinear Schrödinger equations
Pages: 1789  1811,
Issue 4,
April
2016
doi:10.3934/dcds.2016.36.1789 Abstract
References
Full text (496.4K)
Related Articles
Santosh Bhattarai  Trocaire College, Mathematics Department, 360 Choate Ave, Buffalo, NY 14220, United States (email)
1 
J. Albert and J. Angulo, Existence and stability of groundstate solutions of a SchrödingerKdV system, Proc. Royal Soc. of Edinburgh A, 133 (2003), 9871029. 

2 
J. Albert and S. Bhattarai, Existence and stability of a twoparameter family of solitary waves for an NLSKdV system, Adv. Differential Eqns., 18 (2013), 11291164. 

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), 12331260. 

4 
T. B. Benjamin, The stability of solitary waves, Proc. Roy. Soc. London Ser. A, 328 (1972), 153183. 

5 
S. Bhattarai, Solitary waves and a stability analysis for an equation of short and long dispersive waves, Nonlinear Anal., 75 (2012), 65066519. 

6 
S. Bhattarai, Stability of solitarywave solutions of coupled NLS equations with powertype nonlinearities, Adv. Nonlinear Anal., 4 (2015), 7390. 

7 
J. Bona, On the stability theory of solitary waves, Proc. Roy. Soc. London Ser. A, 344 (1975), 363374. 

8 
J. Byeon, Effect of symmetry to the structure of positive solutions in nonlinear elliptic problems, J. Differential Eqns., 163 (2000), 429474. 

9 
T. Cazenave, Semilinear Schrödinger Equations, 10, AMSCourant 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), 549561. 

11 
S. Chakravarty, M. J. Ablowitz, J. R. Sauer and R. B. Jenkins, Multisoliton interactions and wavelengthdivision multiplexing, Opt. Lett., 20 (1995), 136138. 

12 
F. Dalfovo, S. Giorgini, L. P. Pitaevskii and S. Stringari, Theory of BoseEinstein condensation in trapped gases, Rev. Mod. Phys., 71 (1999), 463512. 

13 
T.L. Ho, Spinor Bose condensates in optical traps, Phys. Rev. Lett., 81 (1998), p742. 

14 
Y. Kawaguchi and M. Ueda, Spinor BoseEinstein condensates, Phys. Reports, 520 (2012), 253381. 

15 
E. H. Lieb and M. Loss, Analysis, 2nd ed., 14, AMSGrad. Stud. Math., 2001. 

16 
P. L. Lions, The concentrationcompactness principle in the calculus of variations. The locally compact case, Part 1, Ann. Inst. H. Poincaré Anal. Non Linéaire, 1 (1984), 109145. 

17 
L. F. Mollenauer, S. G. Evangelides and J. P. Gordon, Wavelength division multiplexing with solitons in ultralong transmission using lumped amplifiers, J. Lightwave Technol., 9 (1991), 362367. 

18 
N. V. Nguyen, R.S. Tian, B. Deconinck and N. Sheils, Global existence for a system of Schrödinger equations with powertype nonlinearities, Jour. Math. Phys., 54 (2013), 011503. 

19 
N. V. Nguyen and ZQ. Wang, Orbital stability of solitary waves for a nonlinear Schrodinger system, Adv. Differential Eqns., 16 (2011), 9771000. 

20 
N. V. Nguyen and ZQ. Wang, Orbital stability of solitary waves of a 3coupled nonlinear Schrödinger system, Nonlinear Anal., 90 (2013), 126. 

21 
N. V. Nguyen and ZQ. Wang, Existence and stability of a twoparameter family of solitary waves for a 2coupled nonlinear Schrödinger system, Discrete and Continuous Dynamical Systems  Series A (DCDSA), 36 (2016), 10051021. 

22 
N. V. Nguyen, R. Tian and Z.Q. Wang, Stability of travelingwave solutions for a Schrödinger system with powertype nonlinearities, preprint. 

23 
M. Ohta, Stability of solitary waves for coupled nonlinear Schrödinger equations, Nonlinear Anal., 26 (1996), 933939. 

24 
A. C. Scott, Launching a davydov soliton: I. soliton analysis, Phys. Scr., 29 (1984), p279. 

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), 111114. 

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), 946952. 

27 
T. Tao, Nonlinear Dispersive Equations: Local and Global Analysis, 106 AMSCBMS, 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. 

Go to top
