-
1
-
-
0005235678
-
A topological invariant arising in the stability analysis of traveling waves
-
J.C. Alexander and C.K.R.T. Jones, A topological invariant arising in the stability analysis of traveling waves, J. Reine. Angew. Math., 410 (1990), pp. 167-212.
-
(1990)
J. Reine. Angew. Math.
, vol.410
, pp. 167-212
-
-
Alexander, J.C.1
Jones, C.K.R.T.2
-
2
-
-
0032646251
-
Dynamics of the parametrically driven NLS solitons beyond the onset of the oscillatory instability
-
N. Alexeeva, I. Barashenkov, and D. Pelinovsky, Dynamics of the parametrically driven NLS solitons beyond the onset of the oscillatory instability, Nonlinearity, 12 (1999), pp. 103-140.
-
(1999)
Nonlinearity
, vol.12
, pp. 103-140
-
-
Alexeeva, N.1
Barashenkov, I.2
Pelinovsky, D.3
-
3
-
-
0001367101
-
Variational approach to nonlinear pulse propagation in optical fibers
-
D. Anderson, Variational approach to nonlinear pulse propagation in optical fibers, Phys. Rev. A, 27 (1983), pp. 3135-3144.
-
(1983)
Phys. Rev. A
, vol.27
, pp. 3135-3144
-
-
Anderson, D.1
-
4
-
-
33748109655
-
Existence and persistence of invariant manifolds for semiflows in Banach space
-
P.W. Bates, K. Lu, and C. Zeng, Existence and persistence of invariant manifolds for semiflows in Banach space, Mem. Amer. Math. Soc., 135 (1998).
-
(1998)
Mem. Amer. Math. Soc.
, vol.135
-
-
Bates, P.W.1
Lu, K.2
Zeng, C.3
-
5
-
-
0033409820
-
Persistence of overflowing manifolds for semiflow
-
P.W. Bates, K. Lu, and C. Zeng, Persistence of overflowing manifolds for semiflow, Comm. Pure Appl. Math., 52 (1999), pp. 983-1046.
-
(1999)
Comm. Pure Appl. Math.
, vol.52
, pp. 983-1046
-
-
Bates, P.W.1
Lu, K.2
Zeng, C.3
-
6
-
-
0002538743
-
Invariant manifolds for semilinear partial differential equations
-
P. Bates and C.K.R.T. Jones, Invariant manifolds for semilinear partial differential equations, Dyn. Reported, 2 (1989), pp. 1-38.
-
(1989)
Dyn. Reported
, vol.2
, pp. 1-38
-
-
Bates, P.1
Jones, C.K.R.T.2
-
7
-
-
0000055286
-
Higher order asymptotics of decay for nonlinear, dispersive, dissipative wave, equations
-
J. Bona, K. Promislow, and C.E. Wayne, Higher order asymptotics of decay for nonlinear, dispersive, dissipative wave, equations, Nonlinearity 8, (1995), pp. 1179-1206.
-
(1995)
Nonlinearity
, vol.8
, pp. 1179-1206
-
-
Bona, J.1
Promislow, K.2
Wayne, C.E.3
-
8
-
-
84990739185
-
Renormalization group and asymptotics of solutions of nonlinear parabolic equations
-
J. Bricmont, A. Kupiainen, and G. Lin, Renormalization group and asymptotics of solutions of nonlinear parabolic equations, Comm. Pure Appl. Math., 47 (1994), pp. 893-922.
-
(1994)
Comm. Pure Appl. Math.
, vol.47
, pp. 893-922
-
-
Bricmont, J.1
Kupiainen, A.2
Lin, G.3
-
9
-
-
0012165145
-
Renormalizing partial differential equations, in Constructive Physics
-
Palaiseau, Springer-Verlag, Berlin
-
J. Bricmont and A. Kupiainen, Renormalizing partial differential equations, in Constructive Physics (Palaiseau, 1994), Lecture Notes in Phys., 446, Springer-Verlag, Berlin, 1995, pp. 83-115.
-
(1994)
Lecture Notes in Phys.
, vol.446
, pp. 83-115
-
-
Bricmont, J.1
Kupiainen, A.2
-
12
-
-
21144468600
-
A center-stable manifold theorem for differential equations in Banach spaces
-
T. Gallay, A center-stable manifold theorem for differential equations in Banach spaces, Comm. Math. Phys., 152 (1993), pp. 249-268.
-
(1993)
Comm. Math. Phys.
, vol.152
, pp. 249-268
-
-
Gallay, T.1
-
13
-
-
5344281238
-
Renormalization group and singular perturbations: Multiple scales, boundary layers, and reductive perturbation theory
-
L.Y. Chen, N. Goldenfeld, and Y. Oono, Renormalization group and singular perturbations: Multiple scales, boundary layers, and reductive perturbation theory, Phys. Rev. E (3), 54 (1996), pp. 376-394.
-
(1996)
Phys. Rev. E
, vol.54
, Issue.3
, pp. 376-394
-
-
Chen, L.Y.1
Goldenfeld, N.2
Oono, Y.3
-
14
-
-
0031161337
-
Oscillatory perturbations of the Navier-Stokes equation
-
E. Grenier, Oscillatory perturbations of the Navier-Stokes equation, J. Math. Pures Appl. (9), 76 (1997), pp. 477-498.
-
(1997)
J. Math. Pures Appl.
, vol.76
, Issue.9
, pp. 477-498
-
-
Grenier, E.1
-
15
-
-
0035873348
-
Stabilizing effect of dispersion management
-
E. Grenier, C.K.R.T. Jones, V. Zharnitsky, and S.K. Turitsyn, Stabilizing effect of dispersion management, Phys. D, 152/153 (2001), pp. 794-817.
-
(2001)
Phys. D
, vol.152-153
, pp. 794-817
-
-
Grenier, E.1
Jones, C.K.R.T.2
Zharnitsky, V.3
Turitsyn, S.K.4
-
16
-
-
0003304963
-
The geometric theory of semilinear parabolic equations
-
Springer-Verlag, Berlin
-
D. Henry, The Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Math. 840, Springer-Verlag, Berlin, 1981.
-
(1981)
Lecture Notes in Math.
, vol.840
-
-
Henry, D.1
-
17
-
-
0003123140
-
Quasi-linear equations of evolution, with applications to partial differential equations
-
Spectral Theory and Differential Equations, A. Dold and B. Eckmann, eds., Springer-Verlag, New York
-
T. Kato, Quasi-linear equations of evolution, with applications to partial differential equations, in Spectral Theory and Differential Equations, Lecture Notes in Math. 448, A. Dold and B. Eckmann, eds., Springer-Verlag, New York, pp. 25-70.
-
Lecture Notes in Math.
, vol.448
, pp. 25-70
-
-
Kato, T.1
-
18
-
-
0000425403
-
Soliton evolution and radiation loss for the nonlinear Schrödinger equation
-
W. Kath and N. Smyth, Soliton evolution and radiation loss for the nonlinear Schrödinger equation, Phys. Rev. E (3), 51 (1995), pp. 1484-1492.
-
(1995)
Phys. Rev. E
, vol.51
, Issue.3
, pp. 1484-1492
-
-
Kath, W.1
Smyth, N.2
-
19
-
-
0002348145
-
Stability of bright solitary-wave solutions to perturbed non-linear Schrödinger equations
-
T. Kapitula and B. Sandstede, Stability of bright solitary-wave solutions to perturbed non-linear Schrödinger equations, Phys. D, 124 (1998), pp. 58-103.
-
(1998)
Phys. D
, vol.124
, pp. 58-103
-
-
Kapitula, T.1
Sandstede, B.2
-
20
-
-
84971162773
-
The validity of modulational equations for extended systems with cubic nonlinearities
-
P. Kirrmann, G. Scheinder, and A. Mielke, The validity of modulational equations for extended systems with cubic nonlinearities, Proc. Roy. Soc. Edinburgh Sect. A, 122 (1992), pp. 85-91.
-
(1992)
Proc. Roy. Soc. Edinburgh Sect. A
, vol.122
, pp. 85-91
-
-
Kirrmann, P.1
Scheinder, G.2
Mielke, A.3
-
21
-
-
84975659918
-
Pulse propagation in nonlinear optical fiber-lines that employ phase sensitive parametric amplifiers
-
J.N. Kutz, C.V. Hile, W.L. Kath, R.D. Li, and P. Kumar, Pulse propagation in nonlinear optical fiber-lines that employ phase sensitive parametric amplifiers, J. Opt. Soc. Amer. B Opt. Phys., 11 (1994), pp. 2112-2123.
-
(1994)
J. Opt. Soc. Amer. B Opt. Phys.
, vol.11
, pp. 2112-2123
-
-
Kutz, J.N.1
Hile, C.V.2
Kath, W.L.3
Li, R.D.4
Kumar, P.5
-
22
-
-
0030128338
-
Stability of pulses in nonlinear optical fibers using phase-sensitive amplifiers
-
J.N. Kutz and W.L. Kath, Stability of pulses in nonlinear optical fibers using phase-sensitive amplifiers, SIAM J. Appl. Math., 56 (1996), pp. 611-626.
-
(1996)
SIAM J. Appl. Math.
, vol.56
, pp. 611-626
-
-
Kutz, J.N.1
Kath, W.L.2
-
23
-
-
0000387482
-
Locally invariant manifolds for quasilinear parabolic equations
-
A. Mielke, Locally invariant manifolds for quasilinear parabolic equations, Rocky Mountain J. Math., 21 (1991), pp. 707-714.
-
(1991)
Rocky Mountain J. Math.
, vol.21
, pp. 707-714
-
-
Mielke, A.1
-
24
-
-
21844510556
-
Asymptotic stability of solitary waves
-
R. Pego and M. Weinstein, Asymptotic stability of solitary waves, Comm. Math. Phys., 164 (1994), pp. 305-349.
-
(1994)
Comm. Math. Phys.
, vol.164
, pp. 305-349
-
-
Pego, R.1
Weinstein, M.2
-
25
-
-
0034178760
-
Bifurcation and asymptotic stability in the large detuning limit of the optical parametric oscillator
-
K. Promislow and J.N. Kutz, Bifurcation and asymptotic stability in the large detuning limit of the optical parametric oscillator, Nonlinearity, 13 (2000), pp. 675-698.
-
(2000)
Nonlinearity
, vol.13
, pp. 675-698
-
-
Promislow, K.1
Kutz, J.N.2
-
26
-
-
0032165150
-
Collective coordinates and length-scale competition in spatially inhomogeneous soliton-bearing equations
-
A. Sanchez and A.R. Bishop, Collective coordinates and length-scale competition in spatially inhomogeneous soliton-bearing equations, SIAM Rev., 40 (1998), pp. 579-615.
-
(1998)
SIAM Rev.
, vol.40
, pp. 579-615
-
-
Sanchez, A.1
Bishop, A.R.2
-
27
-
-
21944451412
-
Stability of multiple-pulse solutions
-
B. Sandstede, Stability of multiple-pulse solutions, Trans. Amer. Math. Soc., 350 (1998), pp. 429-472.
-
(1998)
Trans. Amer. Math. Soc.
, vol.350
, pp. 429-472
-
-
Sandstede, B.1
-
29
-
-
0011696958
-
-
private communication, Department of Mathematics, Ohio State University, Columbus, OH, 2001
-
B. Sandstede, private communication, Department of Mathematics, Ohio State University, Columbus, OH, 2001.
-
-
-
Sandstede, B.1
-
30
-
-
0031192318
-
Existence and stability of N-pulses on optical fibers with phase-sensitive amplifiers
-
B. Sandstede, C.K.R.T. Jones, and J.C, Alexander, Existence and stability of N-pulses on optical fibers with phase-sensitive amplifiers, Phys. D, 106 (1997), pp. 167-206.
-
(1997)
Phys. D
, vol.106
, pp. 167-206
-
-
Sandstede, B.1
Jones, C.K.R.T.2
Alexander, J.C.3
-
31
-
-
0001259642
-
Counter-propagating waves on fluid surfaces and the continuum limit of the Fermi-Pasta-Ulam model
-
B. Fielder, K. Gröger, and J. Sprekels, eds., World Scientific, River Edge, NJ
-
G. Schneider and C.E. Wayne, Counter-propagating waves on fluid surfaces and the continuum limit of the Fermi-Pasta-Ulam model, in Equadiff'99: Proceedings of the International Conference on Differential Equations, B. Fielder, K. Gröger, and J. Sprekels, eds., World Scientific, River Edge, NJ, 2000.
-
(2000)
Equadiff'99: Proceedings of the International Conference on Differential Equations
-
-
Schneider, G.1
Wayne, C.E.2
-
32
-
-
0000950086
-
Center manifold theory in infinite dimensions
-
A. Vanderbauwhede and G. Iooss, Center manifold theory in infinite dimensions, Dyn. Reported, 1 (1992), pp. 125-163.
-
(1992)
Dyn. Reported
, vol.1
, pp. 125-163
-
-
Vanderbauwhede, A.1
Iooss, G.2
-
33
-
-
0031282918
-
Invariant manifolds for parabolic partial differential equations on unbounded domains
-
C.E. Wayne, Invariant manifolds for parabolic partial differential equations on unbounded domains, Arch. Ration. Mech. Anal., 138 (1997), pp. 279-306.
-
(1997)
Arch. Ration. Mech. Anal.
, vol.138
, pp. 279-306
-
-
Wayne, C.E.1
-
34
-
-
0001322178
-
Invariant manifolds for a class of dispersive, Hamiltonian, partial differential equations
-
C.A. Pillet and C.E. Wayne, Invariant manifolds for a class of dispersive, Hamiltonian, partial differential equations, J. Differential Equations, 141 (1997), pp. 310-326.
-
(1997)
J. Differential Equations
, vol.141
, pp. 310-326
-
-
Pillet, C.A.1
Wayne, C.E.2
-
35
-
-
0000686130
-
Modulational stability of ground states of nonlinear Schrödinger equations
-
M.I. Weinstein, Modulational stability of ground states of nonlinear Schrödinger equations, SIAM J. Math. Anal., 16 (1985), pp. 472-491.
-
(1985)
SIAM J. Math. Anal.
, vol.16
, pp. 472-491
-
-
Weinstein, M.I.1
-
36
-
-
0004181419
-
Linear and nonlinear waves
-
John Wiley and Sons, New York
-
G.B. Whitham, Linear and Nonlinear Waves, Pure and Applied Mathematics, John Wiley and Sons, New York, 1973.
-
(1973)
Pure and Applied Mathematics
-
-
Whitham, G.B.1
|