Governing equations of envelopes created by nearly bichromatic waves on deep water

Nohara, Ben T.

doi:10.1007/s11071-006-9142-9

Cited by 8 publications

(2 citation statements)

References 15 publications

(14 reference statements)

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“…The MNLS equations are a very important dynamical system in optics and mathematical physics which are used to describe the simultaneous propagation of multi nonlinear waves in a uniform medium and have numerous applications in the areas of plasma physics [4], quantum electronics [5], nonlinear optics [6], Bose-Einstein condensates [7], and hydrodynamics [8]. Recently, many studies have also emerged in fields such as rogue oceanic waves [9], atmosphere [10], and matter waves [11].…”

Section: Introductionmentioning

confidence: 99%

Lie symmetry analysis, exact solutions, and conservation laws to multi-component nonlinear Schrödinger equations

Bai,

Liu,

2023

Nonlinear Dyn

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In this paper, the Lie symmetry group method is used to study the multi-component nonlinear Schrödinger (MNLS) equations in nonlinear mathematical physics. The Lie point symmetries of MNLS equations are obtained. By applying the obtained symmetries, the symmetry reductions and some explicit solutions to the MNLS equations are constructed. In addition, we also find the conservation laws of the MNLS equations using Ibragimov's method.

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Section: Introductionmentioning

confidence: 99%

Lie symmetry analysis, exact solutions, and conservation laws to multi-component nonlinear Schrödinger equations

Bai,

Liu,

2023

Nonlinear Dyn

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“…with appropriate initial conditions U (x, 0) = U 0 , V (x, 0) = V 0 and Dirichlet boundary conditions U (x, t) = f (x), V (x, t) = g(x) on ∂ , where U (x, t), V (x, t) are complex valued functions and K , κ are some constant parameters. The Schrödinger equation has a wide range of applications in the field of Physics, especially in quantum mechanics as follows: water waves, optical pulses, plasma Physics, particle in a box, the harmonic oscillator, the hydrogen atom, the rigid rotator, biomolecular dynamics and many more (Nohara 2007;Argyris and Haase 1987;Kartashov et al 2011;Kivshar and Agrawal 2003;Hasegawa and Tappert 1973;Mollenauer et al 1980;Duree et al 1993). For κ ≥ 0, the existence and uniqueness of global solution for some initial condition u 0 (x) ∈ H 2 ( ) is given by Pazy (page 233).…”

Section: Introductionmentioning

confidence: 99%

A meshfree approach for analysis and computational modeling of non-linear Schrödinger equation

et al. 2020

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In this article, the authors proposed a meshfree approach for simulation of non-linear Schrödinger equation with constant and variable coefficients. Schrödinger equation is a classical field equation whose principal applications are to the propagation of light in non-linear optical fibers and planar waveguides and in quantum mechanics. First of all, spatial derivatives are discretized by using local radial basis functions based on differential quadrature method (LRBF-DQM) and, subsequently, the obtained system of non-linear ordinary differential equations (ODEs) is solved by fourth-order Runge-Kutta (RK-4). The stability analysis of the proposed approach is discussed by the matrix method. Numerical experiments ensure that the proposed approach is accurate and computationally efficient.

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On the quintic nonlinear Schrödinger equation created by the vibrations of a square plate on a weakly nonlinear elastic foundation and the stability of the uniform solution

Nohara¹,

Arimoto

2007

Japan J. Indust. Appl. Math.

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Plates are common structural elements of most engineering structures, including aerospace, automotive, and civil engineering structures. The study of plates from theoretical perspective as well as experimental viewpoint is fundamental to understanding of the behavior of such structures. The dynamic characteristics of plates, such as natural vibrations, transient responses for the external forces and so on, are especially of importance in actual environments. In this paper, we conside the envelope surface created by the vibrations of a square plate on a weakly nonliner elastic foundation and analyze the stability of the uniform solution of the governing equation for the envelope surface. We derive the two-dimensional equation that governs the spatial and temporal evolution of the envelope surface on cubic nonlinear elastic foundation. The fact that the governing equation becomes the quintic nonlinear Schrödinger equation is shown. Also we obtain the stability condition of the uniform solution of the quintic nonlinear Schrödinger equation.

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Governing equations of envelopes created by nearly bichromatic waves on deep water

Cited by 8 publications

References 15 publications

Lie symmetry analysis, exact solutions, and conservation laws to multi-component nonlinear Schrödinger equations

Lie symmetry analysis, exact solutions, and conservation laws to multi-component nonlinear Schrödinger equations

A meshfree approach for analysis and computational modeling of non-linear Schrödinger equation

On the quintic nonlinear Schrödinger equation created by the vibrations of a square plate on a weakly nonlinear elastic foundation and the stability of the uniform solution

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