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We study superregular (SR) breathers (i.e., the quasi-Akhmediev breather collision with a certain phase shift) in a complex modified Korteweg-de Vries equation. We demonstrate that such SR waves can exhibit intriguing nonlinear structures, including the half-transition and full-suppression modes, which have no analogues in the standard nonlinear Schrodinger equation. In contrast to the standard SR breather formed by pairs of quasi-Akhmediev breathers, the half-transition mode describes a mix of quasi-Akhmediev and quasi-periodic waves, whereas the full-suppression mode shows a non-amplifying nonlinear dynamics of localized small perturbations associated with the vanishing growth rate of modulation instability. Interestingly, we show analytically and numerically that these different SR modes can be evolved from an identical localized small perturbation. In particular, our results demonstrate an excellent compatibility relation between SR modes and the linear stability analysis. [ABSTRACT FROM AUTHOR]

We study on rational solutions on nonzero background of coupled Sasa-Satsuma equations through Darboux transformation method, which take into account third-order dispersion, the term with self-frequency shift, and the term describing self-steepening corrections to the cubic nonlinearity. We find there are some new types of localized waves in the coupled system, such as dark-antidark soliton pair, W-shaped soliton, dark W-shaped soliton, and the combined localized waves of them. The results indicate that there are abundant novel localized waves in the two-mode fiber with these high-order effects, which would inspire experimental realization in the related physical systems. [ABSTRACT FROM AUTHOR]

In this paper, we construct a closed form of projectors on the integral noncommutative orbifold T2/Z6 in terms of elliptic functions by GHS (Gopakumar, Headrick and Spradlin) construction. Thereafter, we give a general solution of projectors on T2/Z6 and T2/Z3 with minimal trace and continuous reduced matrix M(k,q0). The projectors constructed by us possess symmetry and manifestly covariant forms under Z6 rotation. Since projectors correspond to the soliton solutions of field theory on the noncommutative orbifold, we thus present a series of corresponding manifestly covariant soliton solutions. [ABSTRACT FROM AUTHOR]

In this paper, we explicitly construct a series of projectors on integrable noncommutative orbifold T[sup 2]/Z[sub 4] by extended GHS construction. They include integration of two arbitary functions with Z[sub 4] symmetry. Our expression possesses manifest Z[sub 4] symmetry. It is proven that the expression includes all projectors with minimal trace and in their standard expansions, the eigenvalue functions of coefficient operators are continuous with respect to the arguments k and q. Based on the integral expression, we alternately show the derivative expression in terms of the similar kernal to the integral one. Since projectors correspond to soliton solutions of the field theory on the noncommutative orbifold, we thus present a series of corresponding solitons. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We report the quantized superfluid vortex filaments induced by the axial flow effect, which exhibit intriguing loop structures on helical vortexes. Such new vortex filaments correspond to a series of soliton excitations including the multipeak soliton, W-shaped soliton, and anti-dark soliton, which have no analogue when the axial flow effect is absent. In particular, we show that the vortex filaments induced by the multipeak soliton and W-shaped soliton arise from the dual action of bending and twisting of the vortex, while the vortex filament induced by the anti-dark soliton is caused only by the bending action, which is consistent with the case of the standard bright soliton. These results will deepen our understanding of breather-induced vortex filaments and will be helpful for controllable ring-like excitations on vortices. [ABSTRACT FROM AUTHOR]

Recently, a report from Elite Readers suggested that a strange phenomenon of ‘square-shaped waves’ had occurred at the beaches of the Isle of Rhe in the Bay of Biscay. Based on the hydrological and geological data of the Bay of Biscay, we find that the special phenomenon is closely related to a solitary wave that can be described by the shallow water wave equation. We discuss the formation mechanisms of the square-shaped waves by the Kadomtsev–Petviashvili equation. The combination of exact solutions and actual condition provides the simulated initial state. We then reproduce a square-shaped structure by a numerical method and obtain the result consistent with the observed picture from media. Our work enriches public understanding of strange water waves and has great significance for tourism development and shipping transportation. [ABSTRACT FROM AUTHOR]

We investigate domain wall excitations in a two-component Bose–Einstein condensate with two-body interactions and pair-transition effects. It is shown that domain wall excitations can be described exactly by kink and anti-kink excitations in each component. The domain wall solutions are given analytically, which exist with different conditions compared with the domain wall reported before. Bubble-droplet structure can be also obtained from the fundamental domain wall, and their interactions are investigated analytically. Especially, domain wall interactions demonstrate some striking particle transition dynamics. These striking transition effects make the domain wall admit quite different collision behavior, in contrast to the collision between solitons or other nonlinear waves. The collisions between kinks induce some phase shift, which makes the domain wall change greatly. Their collisions can be elastic or inelastic with proper combination of fundamental domain walls. These characters can be used to manipulate one domain wall by interacting with other ones. [ABSTRACT FROM AUTHOR]

We study the dynamics of rogue waves on a double-plane wave background in two-component coupled systems. The results indicate that many different patterns can still be evolved from resonant perturbations with the two plane waves background. The obtained vector rational solutions can be decomposed into two rational solutions located on the two plane waves separately. This enables us to investigate the superposition of several well-known fundamental rogue wave patterns, mainly including eye-shaped, anti-eye-shaped, and four-petaled one. The explicit conditions for different possible superpositions are clarified by a phase diagram. The analysis indicates that the obtained rational solution described patterns admit many different profiles, in contrast to the ones reported before. The studies can be extended to investigate other localized waves on double-plane wave backgrounds and even more plane waves involved cases in multi-component coupled systems. [ABSTRACT FROM AUTHOR]

We study the relations between solitons of nonlinear Schrödinger equation and eigen-states of linear Schrödinger equation with some quantum wells. Many different non-degenerated solitons are re-derived from the eigen-states in the quantum wells. We show that the vector solitons for the coupled system with attractive interactions correspond to the identical eigen-states with the ones of the coupled systems with repulsive interactions. Although their energy eigenvalues seem to be different, they can be reduced to identical ones in the same quantum wells. The non-degenerated solitons for multi-component systems can be used to construct much abundant degenerated solitons in more components coupled cases. Meanwhile, we demonstrate that soliton solutions in nonlinear systems can also be used to solve the eigen-problems of quantum wells. As an example, we present the eigenvalue and eigen-state in a complicated quantum well for which the Hamiltonian belongs to the non-Hermitian Hamiltonian having parity–time symmetry. We further present the ground state and the first exited state in an asymmetric quantum double-well from asymmetric solitons. Based on these results, we expect that many nonlinear physical systems can be used to observe the quantum states evolution of quantum wells, such as a water wave tank, nonlinear fiber, Bose–Einstein condensate, and even plasma, although some of them are classical physical systems. These relations provide another way to understand the stability of solitons in nonlinear Schrödinger equation described systems, in contrast to the balance between dispersion and nonlinearity. [ABSTRACT FROM AUTHOR]

We study the nonlinear excitations in the integrable fifth-order nonlinear Schrödinger equation on a continuous wave background. The excited condition of each localized wave is demonstrated via concise phase diagrams. In particular, the rule of transition between asymmetric and symmetric multi-peak solitons is revealed. It is shown that the initial phase modulation can induce the transition and the transition condition is demonstrated exactly. Interestingly, our result shows that although the multi-peak solitons exhibit structural diversity, both the asymmetric and symmetric states possess an identical asymmetric spectrum structure. [ABSTRACT FROM AUTHOR]

We study the interaction between breather and N-order rogue waves in a nonlinear optical fiber. The impacts of the relative phase and the interaction distance between breathers and rogue waves are discussed in detail. Specifically, the breather can reduce the maximum hump value of high-order rogue waves greatly in the cases of nonzero relative phase or nonzero interaction distance. The characteristic of exclusion between breathers and rogue waves is described qualitatively in the situation of different interaction distances, which can be used to change the temporal-spatial distribution of rogue waves. Their interaction properties are characterized by the trajectory of localized waves’ valleys and humps. It is shown that the interaction changes the dynamical evolution trajectory of rogue waves and breathers. These results provide some possible ways to control high-order rogue waves. [ABSTRACT FROM AUTHOR]

We investigate optical superregular breathers in the femtosecond regime under dispersion management in an inhomogeneous fiber governed by the nonautonomous higher-order nonlinear Schrödinger equation (NLSE). Exact solutions describing the dynamics of superregular breathers are obtained. Furthermore, we discuss the propagation behaviors of controllable superregular breathers, including stabilization and recurrence in an exponential dispersion fiber and a periodic distributed fiber system. Particularly, the nonlinear dynamics of superregular modes evolved from an identical initial small-amplitude modulation is analyzed in detail. [ABSTRACT FROM AUTHOR]

We study localized waves on continuous wave background in an exponential dispersion decreasing fiber with two orthogonal polarization states. We demonstrate that asymmetric W-shaped and M-shaped soliton pulse can be generated from a weak modulation on continuous wave background. The numerical simulation results indicate that the generated asymmetric soliton pulses are robust against small noise or perturbation. In particular, the asymmetric degree of the asymmetric soliton pulse can be effectively controlled by changing the relative frequency of the two components. This character can be used to generate other nonlinear localized waves, such as dark–antidark and antidark–dark soliton pulse pair, symmetric W-shaped and M-shaped soliton pulse. Furthermore, we find that the asymmetric soliton pulse possesses an asymmetric discontinuous spectrum. [ABSTRACT FROM AUTHOR]

We study optical localized waves on a plane-wave background in negative-index materials governed by the defocusing nonlinear Schrödinger equation with self-steepening effect. Important characteristics of localized waves, such as the excitations, transitions, propagation stability, and mechanism, are revealed in detail. An intriguing sequential transition that involves the rogue wave, antidark–dark soliton pair, antidark soliton and antidark soliton pair can be triggered as the self-steepening effect attenuates. The corresponding phase diagram is established in the defocusing regime of negative-index materials. The propagation stability of the localized waves is confirmed numerically. In particular, our results illuminate the transition mechanism by establishing the exact correspondence between the transition and the modulation instability analysis. [ABSTRACT FROM AUTHOR]