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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 < ∞.
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
Derivative Nonlinear Schr\"odinger Equation with General Cubic Nonlinearity
"... Nonlinearity(Boundary value problems for partial differential equations) Author(s)KITA, NAOYASU ..."
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Nonlinearity(Boundary value problems for partial differential equations) Author(s)KITA, NAOYASU
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.
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
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
Spatial Evolution of Water Surface Waves: Numerical Simulation and Experiment of Bichromatic Waves
"... The modified nonlinear Schr6dinger (MNLS) equation for spatial evolution of weakly nonlinear water surface waves is shown to yield good comparisons with experimental measurements of bichromatic waves in a long tank. While linear theory does not predict neither the phase velocity nor the evolution of ..."
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Cited by 3 (0 self)
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of the envelope well, the cubic nonlinear Schr6dinger (NLS) equation improves the prediction of the phase velocity but not the modulation of the envelope. The MNLS equation predicts both the evolution of individual wave crests and the modulation of the envelope over longer fetch, and thus permits accurate
NONLINEAR $\mathrm{S}\mathrm{C}\mathrm{H}\mathrm{R}\tilde{\mathrm{O}}$DINGER EQUATIONS IN FRACTIONAL ORDER SOBOLEV SPACES
"... In this note I describe some recent work on nonlinear $\mathrm{S}\mathrm{c}\mathrm{h}\mathrm{r}\tilde{\mathrm{o}}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{e}\mathrm{r} $ equations, done jointly with M. Nakamura $[27, 28] $. We consider the nonlinear Schr\"odinger equations of the form $i\ ..."
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In this note I describe some recent work on nonlinear $\mathrm{S}\mathrm{c}\mathrm{h}\mathrm{r}\tilde{\mathrm{o}}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{e}\mathrm{r} $ equations, done jointly with M. Nakamura $[27, 28] $. We consider the nonlinear Schr\"odinger equations of the form $i
Nonlinear Schrödinger solitons in a periodic structure,’’ Opt
 Incident PeakPower (KW) WSEAS TRANSACTIONS on COMMUNICATIONS Farzin Emami, Amir H. Jafari ISSN: 11092742 685 Issue 7
, 1988
"... It is demonstrated theoretically that a nonlinear medium with a spatially periodic refractive index can support solitons of the nonlinear Schr6dinger equation. In a recent paper ' Winful suggested the use of nonlinear periodic structures for pulse compression and indicated the possibility of ..."
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Cited by 8 (0 self)
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It is demonstrated theoretically that a nonlinear medium with a spatially periodic refractive index can support solitons of the nonlinear Schr6dinger equation. In a recent paper ' Winful suggested the use of nonlinear periodic structures for pulse compression and indicated the possibility
Results 1  10
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34