Bilinearization of the generalized coupled nonlinear Schrödinger equation with variable coefficients and gain and dark-bright pair soliton solutions

Systematic soliton shape modulation by engineering superposed plane wave and soliton parameters

We investigate the linear interference of a plane wave with different localized waves using the coupled Fokas-Lenells equation (FLE) with four-wave mixing term. We obtain the localized wave solution of the coupled FLE by linear superposition of two distinctly independent wave solutions, namely, the plane wave and one soliton solution and the plane wave and two soliton solution. We obtain several nonlinear profiles depending on the relative phase induced by soliton parameters. We present a systematic analysis of the linear interference profile under four different conditions on the spatial and temporal phase coefficients of interfering waves. We further investigate the interaction of two soliton solution and a plane wave. In this case, we find that, asymptotically, two soliton profiles may be similar or different from each other depending on the choices of soliton parameters in the two cases. The present analysis may also be applied to study the linear interference pattern of other localized waves. We believe that the results obtained by us shall be useful in soliton control, all-optical switching, and optical computing.

Gramian solutions and soliton interactions for a generalized (3 + 1)-dimensional variable-coefficient Kadomtsev-Petviashvili equation in a plasma or fluid

Plasmas and fluids are of current interest, supporting a variety of wave phenomena. Plasmas are believed to be possibly the most abundant form of visible matter in the Universe. Investigation in this paper is given to a generalized (3 + 1)-dimensional variable-coefficient Kadomtsev-Petviashvili equation for the nonlinear phenomena in a plasma or fluid. Based on the existing bilinear form, N-soliton solutions in the Gramian are derived, where N = 1, 2, 3…. With N = 3, three-soliton solutions are constructed. Fission and fusion for the three solitons are presented. Effects of the variable coefficients, i.e. h(t), l(t), q(t), n(t) and m(t), on the soliton fission and fusion are revealed: soliton velocity is related to h(t), l(t), q(t), n(t) and m(t), while the soliton amplitude cannot be affected by them, where t is the scaled temporal coordinate, h(t), l(t) and q(t) give the perturbed effects, and m(t) and n(t), respectively, stand for the disturbed wave velocities along two transverse spatial coordinates. We show the three parallel solitons with the same direction.

Phase dynamics of inhomogeneous Manakov vector solitons

We report the exact phase dynamics of Manakov bright and dark vector solitons in an inhomogeneous optical system by means of a variable coefficient coupled nonlinear Schrödinger equation. To investigate the phase dynamics, we have modified the Manakov system with a relation between two modes of propagation, that are obtained by the Hirota bilinear method. The importance of the phase study in soliton interaction is revealed by asymptotic analysis of two-soliton solutions. In contrast with the Manakov bright soliton, the time-dependent dark vector soliton exhibits a gradual phase shift due to the blackness factor. The various inhomogeneous effects on the soliton phase are investigated, with a particular emphasis on nonlinear tunneling. The intensity and corresponding phase of the tunneling soliton either forms a peak or valley and retains its shape after tunneling. Unlike the bright counterpart, the gain or loss term significantly affects the phase of the dark soliton. Apart from the study of soliton intensity, the phase profile of bright and dark vector solitons and its dynamical features are also explored. As the study is not limited to intensity description, the present study could serve as a reference for the future studies on multisolitons phase dynamics in photonics and related fields.

Dynamics of vector dark solitons propagation and tunneling effect in the variable coefficient coupled nonlinear Schrödinger equation

We investigate the dynamics of vector dark solitons propagation using variable coefficient coupled nonlinear Schrödinger (Vc-CNLS) equation. The dark soliton propagation and evolution dynamics in the inhomogeneous system are studied analytically by employing the Hirota bilinear method. It is apparent from our asymptotic analysis that the collision between the dark solitons is elastic in nature. The various inhomogeneous effects on the evolution and interaction between dark solitons are explored, with a particular emphasis on nonlinear tunneling. It is found that the tunneling of the soliton depends on a condition related to the height of the barrier and the amplitude of the soliton. The intensity of the tunneling soliton either forms a peak or a valley, thus retaining its shape after tunneling. For the case of exponential background, the soliton tends to compress after tunneling through the barrier/well. Thus, a comprehensive study of dark soliton pulse evolution and propagation dynamics in Vc-CNLS equation is presented in the paper.

Breather transition dynamics, Peregrine combs and walls, and modulation instability in a variable-coefficient nonlinear Schrödinger equation with higher-order effects

We study a variable-coefficient nonlinear Schrödinger (vc-NLS) equation with higher-order effects. We show that the breather solution can be converted into four types of nonlinear waves on constant backgrounds including the multipeak solitons, antidark soliton, periodic wave, and W-shaped soliton. In particular, the transition condition requiring the group velocity dispersion (GVD) and third-order dispersion (TOD) to scale linearly is obtained analytically. We display several kinds of elastic interactions between the transformed nonlinear waves. We discuss the dispersion management of the multipeak soliton, which indicates that the GVD coefficient controls the number of peaks of the wave while the TOD coefficient has compression effect. The gain or loss has influence on the amplitudes of the multipeak soliton. We further derive the breather multiple births and Peregrine combs by using multiple compression points of Akhmediev breathers and Peregrine rogue waves in optical fiber systems with periodic GVD modulation. In particular, we demonstrate that the Peregrine comb can be converted into a Peregrine wall by the proper choice of the amplitude of the periodic GVD modulation. The Peregrine wall can be seen as an intermediate state between rogue waves and W-shaped solitons. We finally find that the modulational stability regions with zero growth rate coincide with the transition condition using rogue wave eigenvalues. Our results could be useful for the experimental control and manipulation of the formation of generalized Peregrine rogue waves in diverse physical systems modeled by vc-NLS equation with higher-order effects.