Some special solutions to the Hyperbolic NLS equation

Vuillon, Laurent; Dutykh, Denys; Fedele, Francesco

doi:10.1016/j.cnsns.2017.09.018

Cited by 5 publications

(4 citation statements)

References 63 publications

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“…This equation provides a new venue for studying the nonlinear modulation of wave packets described by the nKG model with polynomial nonlinearity involving odd and even powers. Numerical integration can be performed by a variety of techniques, including spectral and pseudo-spectral splitting schemes [20,[49][50][51], the Petviashvili iteration method [18,52,53], the Galerkin finite-element method [54,55] and various finite-difference schemes [56,57]. Further work may also include the study of coupled models, such as the Klein-Gordon-Schrödinger equation [58] used to describe a system of conserved scalar nucleons interacting with neutral scalar mesons or coupled Klein-Gordon equations [59].…”

Section: Discussionmentioning

confidence: 99%

Fifth-order nonlinear Schrödinger equation as Routhian reduction of the nonlinear Klein–Gordon model

Sedletsky,

Gandzha

2023

Proc. R. Soc. A.

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We consider the nonlinear Klein–Gordon model with polynomial nonlinearity involving odd and even powers. We elaborate a hybrid Hamiltonian and Lagrangian approach, which is generally referred to as Routh’s procedure, to describe the nonlinear modulation of wave packets assuming the wave field envelope to be a slow function of time and coordinate. An extended fifth-order nonlinear Schrödinger equation is obtained from the Routhian equation for a complex canonical variable that couples the wave field and its momentum. This canonical variable is expressed in terms of the amplitude of fundamental harmonic and its derivatives with respect to coordinate. The resulting fifth-order nonlinear Schrödinger equation is demonstrated to be a Hamiltonian system under a certain constraint imposed on its model parameters. When compared with other techniques used to derive high-order nonlinear Schrödinger models, our approach preserves the Hamiltonian structure of the governing equations for the fundamental harmonic, while the input of higher harmonics is taken into account by means of variational principle applied to the averaged Routhian. In this way, it represents the most general tool for the reduction of nonlinear wave equations to high-order envelope models for slowly modulated wave packets.

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Section: Discussionmentioning

confidence: 99%

Fifth-order nonlinear Schrödinger equation as Routhian reduction of the nonlinear Klein–Gordon model

Sedletsky,

Gandzha

2023

Proc. R. Soc. A.

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“…The tools used in the analysis are the center manifold reduction and Nash-Moser iteration. The second family of solutions was numerically observed in [51].…”

Section: Solitary Wavesmentioning

confidence: 95%

“…Constructions on nonlocalized, infinite H 1 norm solutions are provided in [14,29,32,36,51]; see [34,Sect. 4.6] for details.…”

Section: Solitary Wavesmentioning

confidence: 99%

On the hyperbolic nonlinear Schrödinger equations

Saut,

Wang

2024

Adv Cont Discr Mod

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“…Equation (8) governs the propagation of modulated waves in a two-dimensional Noguchi nonlinear electrical network with linear dispersion. The type of this equation strongly depends of the sign and magnitude of its dispersion coefficients [62][63][64]. More precisely, the 2D-NLS equation (8) could be elliptic or hyperbolic depending on the values of the coefficients P , 1 P 2 and P 3 [56].…”

Section: Amplitude Equationmentioning

confidence: 99%

Hybrid behavior of a two-dimensional Noguchi nonlinear electrical network

2021

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In this work, the propagation of modulated waves in a nonlinear two-dimensional discrete electrical line is studied. Based on the linear dispersive law, we demonstrate that the network can adopt Hybrid’s behavior due to the fact that, without changing its appearance structure or its parameters values, it can become alternatively, a purely right-handed line, a purely left-handed line or a composite right-left-handed line depending on coupling transverse parameters L 2 , C 2 and k 2 . Using the reductive perturbation method, a (2+1)-dimensional nonlinear Schrodinger equation governing the dynamics of the small amplitude signals in the network is derived and the impact of the above transverse parameters on the sign of the product of their coefficients is examined. Likewise, backward and forward solitary wave propagations in the system is predicted and analyzed quantitatively and qualitatively. The effects of relevant transverse network parameters on the characteristic parameters of these waves are investigated. We find out that these transverse parameters considerably affect the characteristics and the nature of the waves that are propagated throughout the system.

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Some special solutions to the Hyperbolic NLS equation

Cited by 5 publications

References 63 publications

Fifth-order nonlinear Schrödinger equation as Routhian reduction of the nonlinear Klein–Gordon model

Fifth-order nonlinear Schrödinger equation as Routhian reduction of the nonlinear Klein–Gordon model

On the hyperbolic nonlinear Schrödinger equations

Hybrid behavior of a two-dimensional Noguchi nonlinear electrical network

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