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New type of localized solutions for the two-dimensional multicomponent Yajima-Oikawa system is presented. The dynamics of solutions of this type occurs on the zero background and is similar to that of rogue waves.

Exactly Solvable and Integrable Systems · Physics 2024-01-12 N. V. Ustinov

We construct breather and rogue wave solutions of a variable coefficient nonlinear Schr\"odinger equation with an external linear potential. This generalized model describes the nonlinear wave propagation in an inhomogeneous plasma/medium.…

Exactly Solvable and Integrable Systems · Physics 2014-07-14 K. Manikandan , M. Senthilvelan

The long wave-short wave model describes the interaction between the long wave and the short wave. Exact higher-order rational solution expressed by determinants is calculated via the Hirota's bilinear method and the KP hierarchy reduction.…

Exactly Solvable and Integrable Systems · Physics 2019-12-04 Junchao Chen , Liangyuan Chen , Bao-Feng Feng , Ken-ichi Maruno

General dark solitons and mixed solutions consisting of dark solitons and breathers for the third-type Davey-Stewartson (DS-III) equation are derived by employing the bilinear method. By introducing the two differential operators,…

Exactly Solvable and Integrable Systems · Physics 2017-09-13 Jiguang Rao , Kuppuswamy Porsezian , Jingsong He

The dynamics of nonlinear waves with controllable dispersion, nonlinearities, and background continues to be an exciting line of research in recent years. In this work, we focus to investigate an integrable (3+1)-dimensional nonlinear model…

Pattern Formation and Solitons · Physics 2023-02-02 Sudhir Singh , K. Sakkaravarthi , K. Murugesan

Rogue waves in (2+1)-dimensional three-wave resonant interactions are studied. General rogue waves arising from a constant background, from a lump-soliton background and from a dark-soliton background have been derived, and their dynamics…

Exactly Solvable and Integrable Systems · Physics 2022-03-02 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

The solutions of the two-dimensional multicomponent Yajima-Oikawa system that have the functional arbitrariness are constructed by using the Darboux transformation technique. For the zero and constant backgrounds, different types of…

Pattern Formation and Solitons · Physics 2019-12-24 N. V. Ustinov

Due to the widely applications in almost all branches of science, high dimensional KP equation is selected as universal model to describe rogue wave phenomenon. A lump is an algebraically localized wave decayed in all space directions and…

Exactly Solvable and Integrable Systems · Physics 2020-03-27 Man Jia , Senyue Lou

An analytical method for constructing various coherent localized solutions with short-lived characteristics is proposed based on a novel self-mapping transformation of the (2+1) dimensional KdV equation. The highlight of this method is that…

Pattern Formation and Solitons · Physics 2024-05-22 Jie-Fang Zhang , Mei-zhen Jin , Meng-yang Zhang

Rogue waves are abnormally large waves which appear unexpectedly and have attracted considerable attention, particularly in recent years. The one space, one time (1+1) nonlinear Schr\"odinger equation is often used to model rogue waves; it…

Pattern Formation and Solitons · Physics 2021-09-14 Mark J. Ablowitz , Justin T. Cole

Rogue waves in the nonlocal PT-symmetric nonlinear Schrodinger (NLS) equation are studied by Darboux transformation. Three types of rogue waves are derived, and their explicit expressions in terms of Schur polynomials are presented. These…

Exactly Solvable and Integrable Systems · Physics 2018-11-14 Bo Yang , Jianke Yang

We report rogue-wave and lump patterns associated with Umemura polynomials, which arise in rational solutions of the third Painlev\'{e} equation. We first show that in many integrable equations such as the nonlinear Schr\"odinger equation…

Exactly Solvable and Integrable Systems · Physics 2026-04-28 Bo yang , Jianke Yang

The rogue wave solutions (rational multi-breathers) of the nonlinear Schrodinger equation (NLS) are tested in numerical simulations of weakly nonlinear and fully nonlinear hydrodynamic equations. Only the lowest order solutions from 1 to 5…

Fluid Dynamics · Physics 2017-03-30 A. Slunyaev , E. Pelinovsky , A. Sergeeva , A. Chabchoub , N. Hoffmann , M. Onorato , N. Akhmediev

Based on the symbolic computation approach, multiple rogue wave solutions of the generalized (2+1)-dimensional Camassa-Holm-Kadomtsev-Petviashvili equation are studied. As an example, we present the 1-rogue wave solutions, 3-rogue wave…

Pattern Formation and Solitons · Physics 2021-11-04 Jian-Guo Liu , Huan Zhao

The Hirota equation is better than the nonlinear Schr\"{o}dinger equation when approximating deep ocean waves. In this paper, high-order rational solutions for the Hirota equation are constructed based on the parameterized Darboux…

Exactly Solvable and Integrable Systems · Physics 2015-06-15 Linjing Li , Zhiwei Wu , Lihong Wang , Jingsong He

Under investigation is a new (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation. The main results are listed as follows: (i) lump solutions; (ii) Interaction solutions between lump wave and solitary waves; (iii) Interaction solutions…

Pattern Formation and Solitons · Physics 2020-10-27 Jian-Guo Liu , Abdul-Majid Wazwaz

The double-periodic solutions of the focusing nonlinear Schrodinger equation have been previously obtained by the method of separation of variables. We construct these solutions by using an algebraic method with two eigenvalues.…

Exactly Solvable and Integrable Systems · Physics 2019-12-04 Jinbing Chen , Dmitry E. Pelinovsky , Robert E. White

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

In this paper, a variable-coefficient Boiti-Leon-Manna-Pempinelli equation is to be investigated. We obtain abundant multi-wave, breather wave and lump solutions by using the three waves method, the homoclinic breather approach and the…

Pattern Formation and Solitons · Physics 2020-10-27 Jian-Guo Liu , Wang-Ping Xiong