Theoretical and experimental evidence of non-symmetric doubly localized rogue waves

We present determinant expressions for vector rogue wave solutions of the Manakov system, a two-component coupled nonlinear Schr\"odinger equation. As special case, we generate a family of exact and non-symmetric rogue wave solutions of the nonlinear Schr\"odinger equation up to third-order, localized in both space and time. The derived non-symmetric doubly-localized second-order solution is generated experimentally in a water wave flume for deep-water conditions. Experimental results, confirming the characteristic non-symmetric pattern of the solution, are in very good agreement with theory as well as with numerical simulations, based on the modified nonlinear Schr\"odinger equation, known to model accurately the dynamics of weakly nonlinear wave packets in deep-water.Comment: 15 pages, 7 figures, accepted by Proceedings of the Royal Society

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

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

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

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

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