Two-mode Wave Research Articles

Dual-wave of resonant nonlinear Schrödinger's dynamical equation with different nonlinearities

In this work, a new dual-mode nonlinear Schrödinger's equation with Bohm potential is studied with three different forms of nonlinearities. This model has many applications in nonlinear physics and fiber optics. The new model introduces three different physical parameters such as nonlinearity, phase velocity and dispersive factor. This model interprets the simultaneous propagation of two-mode waves instead of a single wave. The singular dual-mode wave solutions are retrieved by versatile exp(-ϕ)-expansion method. The necessary conditions on dissipative nonlinearity parameters that guarantee the existence of soliton solutions are determined. The impact of phase velocity on propagation dynamics of these dual waves is comprehensively studied with the aid of 3D graphs.

Dynamical analysis and phase portraits of two-mode waves in different media

In this work, new dual-mode nonlinear Schrödinger’s equations (NLSEs) are studied with cubic and quadratic cubic nonlinearities. The new models introduce three different physical parameters such as nonlinearity, phase velocity, and dissipative factor. These models interpret the propagation of two-directional waves simultaneously. The necessary conditions on nonlinearity and dissipative factors for the solitons to exist for dual-mode are also calculated. Lastly, to analyze the effect of phase velocity during the promulgation of dual-waves is highlighted graphically. Moreover, the governing model is converted into the planer dynamical system with the help of Galilean transformation. Every possible form of phase portraits is plotted for pertinent parameters viz. k,β,d1,d2,d3. The Runge–Kutta fourth-order technique to extract the nonlinear periodic solutions of the considered problem and outcomes are presented graphically. Furthermore, quasiperiodic and chaotic behavior of p-FLM is analyzed for different values of the parameters upon the application of an after deploying an external periodic force. While, quasiperiodic–chaotic nature is observed for selected values of parameters k,β,d1,d2,d3 by keeping the force and frequency of the perturbed dynamical system fixed.

Two-mode WEC-type attachment for wave energy extraction and reduction of hydroelastic response of pontoon-type VLFS

Proposed herein is a two-mode wave energy converter-type attachment to the fore edge of pontoon-type very large floating structures (VLFSs) for wave energy extraction and reduction of hydroelastic response. This attachment consists of floating horizontal and submerged vertical plates that are connected to the VLFS with hinges and linear power take-off systems. The use of both floating horizontal and submerged vertical plates combines the superior performances of floating plates in extracting wave energy from short waves (T < 5 s) and of submerged vertical plates in extracting wave energy from intermediate and long waves (T > 7 s). When deployed in sites where 5 s ≤ T ≤ 7 s, the two-mode attachment yields a larger power production than the sole usage of floating plates or the sole usage of submerged vertical plates. Interestingly, the two-mode attachment also combines the superior performance of submerged vertical plates in reducing hydroelastic response for relatively short waves (T < 7 s) and the superior performance of floating plates in reducing hydroelastic response for relatively long waves (T ≥ 9 s). Moreover, this two-mode attachment furnishes a good balance between extracting wave energy and reducing hydroelastic response of VLFS for the same wave period.

Mode conversion in cold low-density plasma with a sheared magnetic field

A theory is proposed that describes mutual conversion of two electromagnetic modes in cold low-density plasma, specifically, in the high-frequency limit where the ion response is negligible. In contrast to the classic (Landau–Zener-type) theory of mode conversion, the region of resonant coupling in low-density plasma is not necessarily narrow, so the coupling matrix cannot be approximated with its first-order Taylor expansion; also, the initial conditions are set up differently. For the case of strong magnetic shear, a simple method is identified for preparing a two-mode wave such that it transforms into a single-mode wave upon entering high-density plasma. The theory can be used for reduced modeling of wave-power input in fusion plasmas. In particular, applications are envisioned in stellarator research, where the mutual conversion of two electromagnetic modes near the plasma edge is a known issue.

Multi-soliton solutions and Bäcklund transformation for a two-mode KdV equation in a fluid

In this paper, we investigate a two-mode Korteweg-de Vries equation, which describes the one-dimensional propagation of shallow water waves with two modes in a weakly nonlinear and dispersive fluid system. With the binary Bell polynomial and an auxiliary variable, bilinear forms, multi-soliton solutions in the two-wave modes and Bell polynomial-type Bäcklund transformation for such an equation are obtained through the symbolic computation. Soliton propagation and collisions between the two solitons are presented. Based on the graphic analysis, it is shown that the increase in s can lead to the increase in the soliton velocities under the condition of , but the soliton amplitudes remain unchanged when s changes, where s means the difference between the phase velocities of two-mode waves, and are the nonlinearity parameter and dispersion parameter respectively. Elastic collisions between the two solitons in both two modes are analyzed with the help of graphic analysis.

On wave solutions of a weakly nonlinear and weakly dispersive two-mode wave system

In this paper, we introduce and study rigorously a Hamiltonian structure and soliton solutions for a weakly dissipative and weakly nonlinear medium that governs two Korteweg–de vries (KdV) wave modes. The bounded solution and traveling wave solution such as cnoidal wave and solitary wave are obtained. Subsequently, the equation is numerically solved by Fourier spectral method for its two-soliton solution. These solutions may be useful to explain the nonlinear dynamics of waves for an equation supporting multi-mode weakly dispersive and nonlinear wave medium. In addition, we give an explicit explanation of the mathematics behind the soliton phenomenon for a better understanding of the equation.

Hardy's paradox and the entanglementlike structure of forward-scattered waves

We analyze Hardy's paradox from the point of view of scattering theory. This approach has been useful for the understanding of interaction-free measurement, which is a similar setup. We calculate the forward-scattered waves generated by the beam splitters, which are replaceable in the gedanken experiment. These two-mode waves appear to have an entanglementlike structure.

Two-Mode Wave Solutions to the Degasperis–Procesi Equation

By introducing a new type of solutions, called the multiple-mode wave solutions which can be expressed in nonlinear superposition of single-mode waves with different speeds, we investigate the two-mode wave solutions in Degasperis–Procesi equation and two cases are derived. The explicit expressions for the two-mode waves as well as the existence conditions are presented. It is shown that the two-mode waves may be the nonlinear combinations of many types of single-mode waves, such as periodic waves, solitons, compactons, etc., and more complicated multiple-mode waves can be obtained if higher order or more single-mode waves are taken into consideration. It is pointed out that the two-mode wave solutions can be employed to display the typical mechanism of the interactions between different single-mode waves.

Multiple-mode wave solutions in Vakhnenko equation

A new type of wave solutions, called as multiple-mode waves, which can be expressed in the superposition forms of more than two types of single-mode waves of Vakhnenko equation have been investigated in this Letter. A new general method for obtaining the multiple-mode waves is proposed, based on which four cases of the possible forms of wave solutions with two-mode have been derived. The explicit expressions of the two-mode waves as well as the existence conditions have been presented, which may be the nonlinear combinations between periodic waves, solitons, compactons, etc., with different wave speeds, respectively. It is pointed out that more complicated multiple-mode waves with more than three single-mode waves can be derived accordingly, which can be used to reveal the evolution of interactions between different types of waves, especially between various solitons.

Pulse dynamics in inhomogeneous optically coupled amplifying optical fibers with high-order dispersion effects taken into account

The evolution of the envelope of a two-mode wave packet in an inhomogeneous-over-length amplifying optical fiber is analyzed with the third-order dispersion effects taken into account, the presence of which leads to modulations of one or both edges of the wave packet. High degrees of compression of the pulse and the complete suppression of oscillations of its time envelope can be attained by an appropriate choice of the type of inhomogeneity of the dispersion parameters.

Control of the pulse dynamics in a two-mode nonlinear optical guide with strong intermode coupling

The dynamics of a two-mode wave packet in a nonlinear optical guide is analyzed for the case of arbitrary excitation of the guide in the presence of phase mismatch of the modes forming the wave packet, linear intermode coupling, and self-and cross-modulation interaction. It is shown that existence of a strong intermode coupling allows description of the dynamics of a wave packet by a system of two partial (autonomous) pulses. Soliton and quasi-soliton analytic solutions are obtained for a degenerate (single-partial) solution, and the compression conditions are determined. In the two-partial case, dynamics of the wave packet is studied numerically.

Dynamics of two-mode radiation in optical waveguides with strong mode coupling

Amplitude equations, as well as the effective dispersion and nonlinearity parameters, which define the dynamics of a wave packet formed by two strongly coupled modes, are derived with allowance for the frequency dependence of the linear mode coupling coefficient. These equations are used to study the onset of the modulation instability of the two-mode wave packet, soliton-like pulses, and compression modes. Unlike single-mode systems, the last two effects in optical waveguides may arise for both a negative and positive disper-sion of the waveguide material.

Nonlinear Dynamics of a Two-Mode Wave Packet with Strong Linear Intermode

We investigate the dynamics of the wave packet formed by two codirected strongly interacting waves propagating in a medium with cubic nonlinearity. We obtain a soliton solution of the nonlinear Schrodinger equation in the degenerate case where the wave packet is described by a single partial momentum. In the nondegenerate case, we use the variational method to find the equation for the pulse duration, which turns out to be analogous to the equation for the coordinate in the Kepler problem. Solving it, we find the dependences of the pulse duration on the propagation distance in the cases of “finite” and “infinite” propagation regimes.

Dynamics of optical pulses in periodic nonlinear fibers

Dynamics of a two-mode wave packet with strong linear and nonlinear (cross-modulation) coupling is investigated. The effect of the initial conditions of the pulse excitation on its further transformation is considered. The possibility to control the dispersion parameters of the wave packet by varying the initial conditions of its input is pointed out. The effective parameters of the dispersion and nonlinearity that govern the dynamics of an optical pulse in a periodic nonlinear fiber light guide are obtained.