Liming Ling

High-order rogue waves in vector nonlinear Schrödinger equations.

We study the dynamics of high-order rogue waves (RWs) in two-component coupled nonlinear Schrödinger equations. We find that four fundamental rogue waves can emerge from second-order vector RWs in the coupled system, in contrast to the high-order ones in single-component systems. The distribution shape can be quadrilateral, triangle, and line structures by varying the proper initial excitations given by the exact analytical solutions. The distribution pattern for vector RWs is more abundant than that for scalar rogue waves. Possibilities to observe these new patterns for rogue waves are discussed for a nonlinear fiber.

Darboux transformation and multi-dark soliton for N-component nonlinear Schrödinger equations

In this paper, we obtain a uniform Darboux transformation for multi-component coupled NLS equations, which can be reduced to all previous presented Darboux transformation. As a direct application, we derive the single dark soliton and multi-dark soliton solutions for multi-component coupled NLS with defocusing case and mixed focusing and defocusing case. Some exact single and two-dark solitons of three-component NLS equation are shown by plotting the picture.

Darboux transformation and classification of solution for mixed coupled nonlinear Schrödinger equations

Abstract We derive generalized localized wave solution formula for mixed coupled nonlinear Schodinger equations (mCNLSE) by performing the unified Darboux transformation. Based on the dynamical behavior of solution, the classification of the localized wave solutions on the nonzero background is given explicitly. Especially, the parameter conditions for breather, dark soliton and rogue wave solution of mCNLSE are given in detail. Moreover, we analyze the interaction between dark soliton solution and breather solution. These results would be helpful for nonlinear localized wave excitations and applications in vector nonlinear systems.

High-order rogue wave solutions for the coupled nonlinear Schrödinger equations-II

We study on dynamics of high-order rogue wave in two-component coupled nonlinear Schrodinger equations. Based on the generalized Darboux transformation and formal series method, we obtain the high-order rogue wave solution without the special limitation on the wave vectors. As an application, we exhibit the first, second-order rogue wave solutions and the superposition of them by computer plotting. We find the distribution patterns for vector rogue waves are much more abundant than the ones for scalar rogue waves, and also different from the ones obtained with the constrain conditions on background fields. The results further enrich and deepen our realization on rogue wave excitation dynamics in such diverse fields as Bose-Einstein condensates, nonlinear fibers, and superfluids.

Collisional dynamics of solitons in the coupled PT symmetric nonlocal nonlinear Schrödinger equations

Abstract We investigate the focussing coupled PT symmetric nonlocal nonlinear Schrodinger equation employing Darboux transformation approach. We find a family of exact solutions including pairs of Bright-Bright, Dark-Dark and Bright-Dark solitons in addition to solitary waves. We show that one can convert bright bound state onto a dark bound state in a two soliton solution by selectively finetuning the amplitude dependent parameter. We also show that the energy in each mode remains conserved unlike the celebrated Manakov model. We also characterize the behaviour of the soliton solutions in detail. We emphasize that the above phenomenon occurs due to the nonlocality of the model.

Generation mechanisms of fundamental rogue wave spatial-temporal structure

We discuss the generation mechanism of fundamental rogue wave structures in N-component coupled systems, based on analytical solutions of the nonlinear Schrödinger equation and modulational instability analysis. Our analysis discloses that the pattern of a fundamental rogue wave is determined by the evolution energy and growth rate of the resonant perturbation that is responsible for forming the rogue wave. This finding allows one to predict the rogue wave pattern without the need to solve the N-component coupled nonlinear Schrödinger equation. Furthermore, our results show that N-component coupled nonlinear Schrödinger systems may possess N different fundamental rogue wave patterns at most. These results can be extended to evaluate the type and number of fundamental rogue wave structure in other coupled nonlinear systems.

Dynamics of rogue wave excitation pattern on stripe phase backgrounds in a two-component Bose-Einstein condensate

Abstract We study rogue wave excitation pattern in a two-component Bose-Einstein condensate with pair-transition effects. The results indicate that rogue wave excitation can exist on a stripe phase background for which there are cosine and sine wave background in the two components respectively. The rogue wave peak can be much lower than the ones of scalar matter wave rogue waves, and varies with the wave period changing. Both rogue wave pattern and rogue wave number on temporal-spatial plane are much more abundant than the ones reported before. Furthermore, we prove that the rogue wave number can be n ( n + 1 ) / 2 + m ( m + 1 ) / 2 (where m, n are arbitrary non-negative integers), in contrast to n ( n + 1 ) / 2 for scalar nonlinear Schrodinger equation described systems. These results would enrich our knowledge on nonlinear excitations in multi-component Bose-Einstein condensate with transition coupling effects.

Tunneling dynamics between atomic bright solitons

We investigate tunneling behavior between two bright solitons in a Bose–Einstein condensate with attractive contact interactions between atoms. The explicit tunneling properties including tunneling particles and oscillation period are described analytically, which indicates that the periodic tunneling form is a nonlinear Josephson type oscillation. The results suggest that the breathing behavior of solitons comes from the tunneling mechanism in an effective double-well potential, which is quite different from the modulational instability mechanism for Akhmediev breather and K-M breather. The relative phase between the two solitons has no effects on the tunneling period and particle exchanging rate. Furthermore, we obtain a phase diagram for two-soliton interaction which admits tunneling property, particle-like property, interference property, and a resonant interaction case. The explicit conditions for them are clarified based on the defined critical distance

Mechanism of Kuznetsov-Ma breathers

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