Results 1  10
of
168
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 < ∞. ..."
Abstract

Cited by 83 (2 self)
 Add to MetaCart
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 < ∞.
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 ..."
Abstract
 Add to MetaCart
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 the criteria for the stability are obtained. The long time evolution of the solutions to the coupled system is studied numerically for the unstable case emphasizing wavewave interactions in nonlinear optics. Different kinds of evolution are observed depending on the coefficients of the system and the parameters of the unperturbed waves and perturbation. For certain ranges of parameters, the evolution appears to be periodic, while for some other ranges of parameters, solitary wave or solitary wave pairs can be excited among the irregular
A THEOREM ON "LOCALIZED" SELFADJOINTNESS OF $CHRDINGER OPERATORS WITH L [ocPOTENTIALS
, 1982
"... ABSTRACT. We prove a result which concludes the selfadjointness of a Schr6"dinger operator from the selfadjointness of the associated "localized" Schr6"dinger oper ..."
Abstract
 Add to MetaCart
ABSTRACT. We prove a result which concludes the selfadjointness of a Schr6"dinger operator from the selfadjointness of the associated "localized" Schr6"dinger oper
Ph'YSICA Vector nonlinear Schr6dinger hierarchies as approximate KadomtsevPetviashvili hierarchies
, 1997
"... Abstract The KadomtsevPetviashvili (KP) hierarchy, a collection of compatible nonlinear equations, each in 2 + 1 independent variables, can be consistently constrained in many different ways to yield hierarchies of equations in 1 + 1 independent variables. In particular, the Ncomponent vector non ..."
Abstract
 Add to MetaCart
nonlinear Schr6dinger (VNLS) hierarchies are contained within the KP hierarchy in this way. These hierarchies approximate the KP hierarchy in the limit of large N, and this permits the equations of the KP hierarchy to be approximated by nonlinear equations in 1 + 1 dimensions.
NorthHolland Optical turbulence: weak turbulence, condensates and collapsing filaments in the nonlinear Schr6dinger equation*
, 1991
"... The nonlinear Schr6dinger (NLS) equation i ~ t + V2 ~ + al~lS ~ = 0 is a canonical and universal equation which is of major importance in continuum echanics, plasma physics and optics. This paper argues that much of the observed solution behavior in the critical case sd = 4, where d is dimension an ..."
Abstract
 Add to MetaCart
The nonlinear Schr6dinger (NLS) equation i ~ t + V2 ~ + al~lS ~ = 0 is a canonical and universal equation which is of major importance in continuum echanics, plasma physics and optics. This paper argues that much of the observed solution behavior in the critical case sd = 4, where d is dimension
On fundamental solutions of generalized Schro$ dinger operators
 J. Funct. Anal
, 1999
"... We consider the generalized Schro dinger operator &2++, where + is a nonnegative Radon measure in R n , n 3. Assuming that + satisfies certain scaleinvariant Kato conditions and doubling conditions we establish the following bounds for the fundamental solution of &2++ in R n , where d(x, y ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
We consider the generalized Schro dinger operator &2++, where + is a nonnegative Radon measure in R n , n 3. Assuming that + satisfies certain scaleinvariant Kato conditions and doubling conditions we establish the following bounds for the fundamental solution of &2++ in R n , where d
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 ..."
Abstract
 Add to MetaCart
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 invariant tends to zero exponentially fast in the adiabatic limit.
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 ..."
Abstract
 Add to MetaCart
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 soliton perturbations is found. Using this solution, an expression for the stability characteristic is deduced, which, in the case of unstable solitons, determines their decay length and, in the case of stable solitons, shows the presence of perturbations with anomalously weak damping (internal modes) and determines their oscillation period. © 2000 MAIK "Nauka/Interperiodica".
Results 1  10
of
168