English
Related papers

Related papers: Rational solutions to multicomponent Yajima-Oikawa…

200 papers

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…

Pattern Formation and Solitons · Physics 2015-01-26 Liming Ling , Boling Guo , Li-Chen Zhao

General high-order rogue waves in the nonlinear Schroedinger equation are derived by the bilinear method. These rogue waves are given in terms of determinants whose matrix elements have simple algebraic expressions. It is shown that the…

Exactly Solvable and Integrable Systems · Physics 2015-05-30 Yasuhiro Ohta , Jianke Yang

We show that universal rogue wave patterns exist in integrable systems. These rogue patterns comprise fundamental rogue waves arranged in shapes such as triangle, pentagon and heptagon, with a possible lower-order rogue wave at the center.…

Exactly Solvable and Integrable Systems · Physics 2021-07-14 Bo Yang , Jianke Yang

In multi-component systems, several rogue waves can be simultaneously excited using simple initial conditions in the form of a plane wave with a small amplitude single-peak perturbation. This is in drastic contrast with the case of…

Pattern Formation and Solitons · Physics 2022-03-09 Chong Liu , Shao-Chun Chen , Xiankun Yao , Nail Akhmediev

In this work, we construct various interesting localized wave structures of the Benjamin-Ono equation describing the dynamics of deep water waves. Particularly, we extract the rogue waves and generalized breather solutions with the aid of…

Exactly Solvable and Integrable Systems · Physics 2020-11-03 Sudhir Singh , K. Sakkaravarthi , K. Murugesan , R. Sakthivel

This work deals with the dynamics of higher-order rogue waves in a new integrable (2+1)-dimensional Boussinesq equation governing the evolution of high and steep gravity water waves. To achieve this objective, we construct rogue wave…

Exactly Solvable and Integrable Systems · Physics 2020-11-03 Sudhir Singh , Lakhveer Kaur , K. Sakkaravarthi , R. Sakthivel , K. Murugesan

In this work, we focus on the construction of Nth-rouge wave solutions for the Hirota equation by utilizing the bilinear method. The formula can be represented in terms of determinants. In addition, some interesting dynamic patterns of…

Exactly Solvable and Integrable Systems · Physics 2014-09-24 Gui Mu , Zhenyun Qin

An integrable system of two-component nonlinear Ablowitz-Ladik (AL) equations is used to construct complex rogue-wave (RW) solutions in an explicit form. First, the modulational instability of continuous waves is studied in the system.…

Exactly Solvable and Integrable Systems · Physics 2017-03-31 Xiao-Yong Wen , Zhenya Yan , Boris A. Malomed

We investigate rogue-wave solutions in a three-component coupled nonlinear Schrodinger equation. With certain requirements on the backgrounds of components, we construct a multi-rogue-wave solution that exhibits a structure like a…

Pattern Formation and Solitons · Physics 2015-01-26 Li-Chen Zhao , Jie Liu

A Jimbo-Miwa like nonlinear differential equation in (3+1)-dimensions is developed through a generalized bilinear equation with the generalized bilinear derivatives. Based on the generalized bilinear forms, two classes of lump solutions,…

Exactly Solvable and Integrable Systems · Physics 2016-11-15 Harun-Or-Roshid , M. Zulfikar Ali

Rogue wave patterns in the nonlinear Schr\"{o}dinger (NLS) equation and the derivative NLS equation are analytically studied. It is shown that when the free parameters in the analytical expressions of these rogue waves are large, these…

Pattern Formation and Solitons · Physics 2020-09-15 Bo Yang , Jianke Yang

In this paper, the PT -symmetric version of the Maccari system is introduced, which can be regarded as a two-dimensional generalization of the defocusing nonlocal nonlinear Schrodinger equation. Various exact solutions of the nonlocal…

Exactly Solvable and Integrable Systems · Physics 2020-12-29 Yulei Cao , Yi Cheng , Boris A. Malomed , Jingsong He

We construct rogue wave solutions on the double periodic background for the Hirota equation through one fold Darboux transformation formula. We consider two types of double periodic solutions as seed solutions. We identify the squared…

Pattern Formation and Solitons · Physics 2021-02-10 N. Sinthuja , K. Manikandan , M. Senthilvelan

General rogue waves in the focusing and defocusing Ablowitz-Ladik equations are derived by the bilinear method. In the focusing case, it is shown that rogue waves are always bounded. In addition, fundamental rogue waves reach peak…

Exactly Solvable and Integrable Systems · Physics 2015-06-18 Yasuhiro Ohta , Jianke Yang

Based on modulation instability analysis and generalized Darboux transformation, we derive a hierarchy of rogue wave solutions for a variable-coefficients coupled Hirota equations. The explicit first-order rogue wave solution is presented,…

Exactly Solvable and Integrable Systems · Physics 2015-12-29 Xin Wang , Yong Chen

Riemann theta functions are used to construct one-periodic and two-periodic wave solutions to a class of (2+1)-dimensional Hirota bilinear equations. The basis for the involved solution analysis is the Hirota bilinear formulation, and the…

Exactly Solvable and Integrable Systems · Physics 2015-05-13 Wen-Xiu Ma , Ruguang Zhou , Liang Gao

Spatially-bounded rogue waves, i.e., rogue waves that arise in a limited region of a multi-dimensional space, are interesting and important from both theoretical and applied points of view. In this paper, we determine spatially-bounded…

Exactly Solvable and Integrable Systems · Physics 2025-11-24 Bo Yang , Jianke Yang

Rogue wave patterns in the nonlinear Schr\"{o}dinger equation are analytically studied. It is shown that when an internal parameter in the rogue waves (which controls the shape of initial weak perturbations to the uniform background) is…

Exactly Solvable and Integrable Systems · Physics 2021-01-06 Bo Yang , Jianke Yang

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…

Pattern Formation and Solitons · Physics 2016-05-31 Li-Chen Zhao , Boling Guo , Liming Ling

In this paper, a modified symbolic computation approach is proposed. The multiple rogue wave solutions of a generalized (2+1)-dimensional Boussinesq equation are obtained by using the modified symbolic computation approach. Dynamics…

Mathematical Physics · Physics 2020-10-27 Jian-Guo Liu , Wen-Hui Zhu