188 research outputs found

    Rogue waves of the Fokas-Lenells equation

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    The Fokas-Lenells (FL) equation arises as a model eqution which describes for nonlinear pulse propagation in optical fibers by retaining terms up to the next leading asymptotic order (in the leading asymptotic order the nonlinear Schr\"odinger (NLS) equation results). Here we present an explicit analytical representation for the rogue waves of the FL equation. This representation is constructed by deriving an appropriate Darboux transformation (DT) and utilizing a Taylor series expansion of the associated breather solution. when certain higher-order nonlinear effects are considered, the propagation of rogue waves in optical fibers is given.Comment: 7 pages, 3 figure

    The hierarchy of higher order solutions of the derivative nonlinear Schr\"odinger equation

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    In this paper, we provide a simple method to generate higher order position solutions and rogue wave solutions for the derivative nonlinear Schr\"odinger equation. The formulae of these higher order solutions are given in terms of determinants. The dynamics and structures of solutions generated by this method are studied

    The higher order Rogue Wave solutions of the Gerdjikov-Ivanov equation

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    We construct higher order rogue wave solutions for the Gerdjikov-Ivanov equation explicitly in term of determinant expression. Dynamics of both soliton and non-soliton solutions is discussed. A family of solutions with distinct structures are presented, which are new to the Gerdjikov-Ivanov equation

    Compare More Nuanced:Pairwise Alignment Bilinear Network For Few-shot Fine-grained Learning

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    The recognition ability of human beings is developed in a progressive way. Usually, children learn to discriminate various objects from coarse to fine-grained with limited supervision. Inspired by this learning process, we propose a simple yet effective model for the Few-Shot Fine-Grained (FSFG) recognition, which tries to tackle the challenging fine-grained recognition task using meta-learning. The proposed method, named Pairwise Alignment Bilinear Network (PABN), is an end-to-end deep neural network. Unlike traditional deep bilinear networks for fine-grained classification, which adopt the self-bilinear pooling to capture the subtle features of images, the proposed model uses a novel pairwise bilinear pooling to compare the nuanced differences between base images and query images for learning a deep distance metric. In order to match base image features with query image features, we design feature alignment losses before the proposed pairwise bilinear pooling. Experiment results on four fine-grained classification datasets and one generic few-shot dataset demonstrate that the proposed model outperforms both the state-ofthe-art few-shot fine-grained and general few-shot methods.Comment: ICME 2019 Ora