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Invariant Cantor manifolds of quasiperiodic oscillations for a nonlinear Schr6dinger equation
"... This paper is concerned with the nonlinear Schrödinger equation iut = uxx − mu − f (u2)u, (1) on the finite xinterval [0, π] with Dirichlet boundary conditions u(t, 0) = 0 = u(t, π), − ∞ < t < ∞. ..."
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Cited by 83 (2 self)
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This paper is concerned with the nonlinear Schrödinger equation iut = uxx − mu − f (u2)u, (1) on the finite xinterval [0, π] with Dirichlet boundary conditions u(t, 0) = 0 = u(t, π), − ∞ < t < ∞.
NorthHolland Optical turbulence: weak turbulence, condensates and collapsing filaments in the nonlinear Schr6dinger equation*
, 1991
"... The nonlinear Schr6dinger (NLS) equation i ~ t + V2 ~ + al~lS ~ = 0 is a canonical and universal equation which is of major importance in continuum echanics, plasma physics and optics. This paper argues that much of the observed solution behavior in the critical case sd = 4, where d is dimension an ..."
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The nonlinear Schr6dinger (NLS) equation i ~ t + V2 ~ + al~lS ~ = 0 is a canonical and universal equation which is of major importance in continuum echanics, plasma physics and optics. This paper argues that much of the observed solution behavior in the critical case sd = 4, where d is dimension
Semilinear
"... parabolic equation on bounded domain with critical Sobolev exponent Takashi SUZUKI (Osaka Univ.) The semilinear parabolic equation ut −∆u = up−1 u in Ω × (0, T), u∂Ω = 0, ut=0 = u0(x) (1) was introduced pure mathematically, but its profiles of the solution, particularly blowup in finite and inf ..."
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parabolic equation on bounded domain with critical Sobolev exponent Takashi SUZUKI (Osaka Univ.) The semilinear parabolic equation ut −∆u = up−1 u in Ω × (0, T), u∂Ω = 0, ut=0 = u0(x) (1) was introduced pure mathematically, but its profiles of the solution, particularly blowup in finite and in
The two coupled nonlinear Schrdinger equations (CNLS, hereafter) are
, 1999
"... The system of two coupled nonlinear Schrödinger equations has wide applications in physics. In the past, the main attention has been their solitary waves. Here we turn our attention to their periodic wave solutions. In this paper, the stability of the periodic solutions is studied analytically and t ..."
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The system of two coupled nonlinear Schrödinger equations has wide applications in physics. In the past, the main attention has been their solitary waves. Here we turn our attention to their periodic wave solutions. In this paper, the stability of the periodic solutions is studied analytically
On the focusing critical semilinear wave equation
 AMER. JOURNAL MATH
"... in R 3 is known to exhibit finite time blowup for data of negative energy. It also admits the special static solutions φ(x, a) = (3a) 1 4 (1 + ax  2) − 1 2 for all a> 0 which are linearly unstable. We view these functions as a curve in the energy space ˙ H 1 × L 2. We show that in a small nei ..."
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Cited by 49 (16 self)
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in R 3 is known to exhibit finite time blowup for data of negative energy. It also admits the special static solutions φ(x, a) = (3a) 1 4 (1 + ax  2) − 1 2 for all a> 0 which are linearly unstable. We view these functions as a curve in the energy space ˙ H 1 × L 2. We show that in a small neighborhood of itself, which lies on a stable hypersurface of radial data, this curve acts as a onedimensional attractor.
Ground states and concentration phenomena for the fractional schr?dinger equation. arXiv:1411.0576
"... ar ..."
Communications in Mathematical Physics Exponentially Small Adiabatic Invariant for the Schr6dinger Equation*
, 1991
"... Abstract. We study an adiabatic invariant for the timedependent Schrfdinger equation which gives the transition probability across a gap from time t' to time t. When the hamiltonian depends analytically on time, and t' = oo, t = + oo we give sufficient conditions so that this adiabatic ..."
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Abstract. We study an adiabatic invariant for the timedependent Schrfdinger equation which gives the transition probability across a gap from time t' to time t. When the hamiltonian depends analytically on time, and t' = oo, t = + oo we give sufficient conditions so that this adiabatic
Stability and oscillations of twodimensional solitons described by the perturbed nonlinear Schrödinger equation
"... Abstract A perturbation theory for determining the stability characteristics of spatial optical solitons with a 2D transverse profile in a transparent medium with a weak saturation of nonlinear refractive index is developed. For Kerr nonlinearity, a new solution of linearized equations for weak so ..."
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Abstract A perturbation theory for determining the stability characteristics of spatial optical solitons with a 2D transverse profile in a transparent medium with a weak saturation of nonlinear refractive index is developed. For Kerr nonlinearity, a new solution of linearized equations for weak
Ph'YSICA Vector nonlinear Schr6dinger hierarchies as approximate KadomtsevPetviashvili hierarchies
, 1997
"... Abstract The KadomtsevPetviashvili (KP) hierarchy, a collection of compatible nonlinear equations, each in 2 + 1 independent variables, can be consistently constrained in many different ways to yield hierarchies of equations in 1 + 1 independent variables. In particular, the Ncomponent vector non ..."
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nonlinear Schr6dinger (VNLS) hierarchies are contained within the KP hierarchy in this way. These hierarchies approximate the KP hierarchy in the limit of large N, and this permits the equations of the KP hierarchy to be approximated by nonlinear equations in 1 + 1 dimensions.
Results 1  10
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269