Mixed soliton solutions of the defocusing nonlocal nonlinear Schrodinger equation

By using the Darboux transformation, we obtain two new types of exponential-and-rational mixed soliton solutions for the defocusing nonlocal nonlinear Schrodinger equation. We reveal that the first type of solution can display a large variety of interactions among two exponential solitons and two rational solitons, in which the standard elastic interaction properties are preserved and each soliton could be either the dark or antidark type. By developing the asymptotic analysis technique, we also find that the second type of solution can exhibit the elastic interactions among four mixed asymptotic solitons. But in sharp contrast to the common solitons, the asymptotic mixed solitons have the t-dependent velocities and their phase shifts before and after interaction also grow with |t| in the logarithmical manner. In addition, we discuss the degenerate cases for such two types of mixed soliton solutions when the four-soliton interaction reduces to a three-soliton or two-soliton interaction.Comment: 28 pages, 7 figure

Statistically induced topological phase transitions in a one-dimensional superlattice anyon-Hubbard model

We theoretically investigate topological properties of the one-dimensional superlattice anyon-Hubbard model, which can be mapped to a superlattice bose-Hubbard model with an occupation-dependent phase factor by fractional Jordan-Wigner transformation. The topological anyon-Mott insulator is identified by topological invariant and edge modes using exact diagonalization and density-matrix renormalization-group algorithm. When only the statistical angle is varied and all other parameters are fixed, a statistically induced topological phase transition can be realized, which provides new insights into the topological phase transitions. What's more, we give an explanation of the statistically induced topological phase transition. The topological anyon-Mott phases can also appear in a variety of superlattice anyon-Hubbard models.Comment: 7 pages, 8 figures, comments are welcom

Stochastic collocation methods via minimization of Transformed L1L_1 penalty

We study the properties of sparse reconstruction of transformed $\ell_1$ (TL1) minimization and present improved theoretical results about the recoverability and the accuracy of this reconstruction from undersampled measurements. We then combine this method with the stochastic collocation approach to identify the coefficients of sparse orthogonal polynomial expansions for uncertainty quantification. In order to implement the TL1 minimization, we use the DCA-TL1 algorithm which was introduced by Zhang and Xin. In particular, when recover non-sparse functions, we adopt an adaptive DCA-TL1 method to guarantee the sparest solutions. Various numerical examples, including sparse polynomial functions recovery and non-sparse analytical functions recovery are presented to demonstrate the recoverability and efficiency of this novel method and its potential for problems of practical interests.Comment: 18 pages, 8 figure

The applications of the general and reduced Yangian algebras

The applications of the general and reduced Yangian Y(sl(2)) and Y(su(3)) algebras are discussed. By taking a special constraint, the representation of Y(sl(2)) and Y(su(3)) can be divided into two 2 \times 2 and three 3 \times 3 blocks diagonal respectively. The general and reduced Yangian Y(sl(2)) and Y(su(3)) are applied to the bi-qubit system and the mixed light pseudoscalar meson state, respectively. We can find that the general ones are not able to make the initial states disentangled by acting on the initial states, however the reduced ones are able to make the initial state disentangled. In addition, we show the effects of Y(su(3)) generators on the the decay channel

High-order Rogue Waves in Vector Nonlinear Schr\"odinger Equations

We study on dynamics of high-order rogue wave in two-component coupled nonlinear Schr\"{o}dinger equations. We find four fundamental rogue waves can emerge for second-order vector RW 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 through varying the proper initial excitations given by the exact analytical solutions. Moreover, six fundamental rogue wave can emerge on the distribution for second-order vector rogue wave, which is similar to the scalar third-order ones. The distribution patten for vector ones are much abundant than the ones for scalar rogue waves. The results could be of interest in such diverse fields as Bose-Einstein condensates, nonlinear fibers, and superfluids.Comment: 5 pages, 4 figure

Darboux transformation and multi-dark soliton for N-component coupled nonlinear Schr\"odinger 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.Comment: 14 pages, 4 figure

Reply to "Comment on "Darboux transformation and classification of solution for mixed coupled nonlinear Schr\"odinger equations""

In the recent comment quoted in the title (arXiv:1407.7852v1), a comment is presented on our recent work which derive a generalized nonlinear wave solution formula for mixed coupled nonlinear Sch\"{o}dinger equations by performing the unified Darboux transformation (arXiv:1407.5194). Here we would like to reply to the comment and clarify some facts in arXiv:1407.5194

High-order Rogue Wave solutions for the Coupled Nonlinear Schr\"{o}dinger Equations-II

We study on dynamics of high-order rogue wave in two-component coupled nonlinear Schr\"{o}dinger 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 solution 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 deep our realization on rogue wave excitation dynamics in such diverse fields as Bose-Einstein condensates, nonlinear fibers, and superfluids.Comment: 9 pages, 7 figure

Darboux transformation and classification of solution for mixed coupled nonlinear Schr\"odinger equations

We derive generalized nonlinear wave solution formula for mixed coupled nonlinear Sch\"odinger equations (mCNLSE) by performing the unified Darboux transformation. We give the classification of the general soliton formula on the nonzero background based on the dynamical behavior. Especially, the conditions for breather, dark soliton and rogue wave solution for mCNLSE are given in detail. Moreover, we analysis the interaction between dark-dark soliton solution and breather solution. These results would be helpful for nonlinear localized wave excitations and applications in vector nonlinear systems.Comment: 28 pages, 9 figure

Efficient Deterministic Replay Using Complete Race Detection

Data races can significantly affect the executions of multi-threaded programs. Hence, one has to recur the results of data races to deterministically replay a multi-threaded program. However, data races are concealed in enormous number of memory operations in a program. Due to the difficulty of accurately identifying data races, previous multi-threaded deterministic record/replay schemes for commodity multi-processor system give up to record data races directly. Consequently, they either record all shared memory operations, which brings remarkable slowdown to the production run, or record the synchronization only, which introduces significant efforts to replay. Inspired by the advances in data race detection, we propose an efficient software-only deterministic replay scheme for commodity multi-processor systems, which is named RacX. The key insight of RacX is as follows: although it is NP-hard to accurately identify the existence of data races between a pair of memory operations, we can find out all potential data races in a multi-threaded program, in which the false positives can be reduced to a small amount with our automatic false positive reduction techniques. As a result, RacX can efficiently monitor all potential data races to deterministically replay a multi-threaded program. To evaluate RacX, we have carried out experiments over a number of well-known multi-threaded programs from SPLASH-2 benchmark suite and large-scale commercial programs. RacX can precisely recur production runs of these programs with value determinism. Averagely, RacX causes only about 1.21%, 1.89%, 2.20%, and 8.41% slowdown to the original run during recording (for 2-, 4-, 8- and 16-thread programs, respectively). The soundness, efficiency, scalability, and portability of RacX well demonstrate its superiority.Comment: 18 pages, 7 figure