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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 study to unify soliton systems, KdV/mKdV/sinh-Gordon, through SO(2,1) $\cong$ GL(2,$\mathbb R$) $\cong$ M\"{o}bius group point of view, which might be a keystone to exactly solve some special non-linear differential equations. If we…

Exactly Solvable and Integrable Systems · Physics 2020-04-08 Masahito Hayashi , Kazuyasu Shigemoto , Takuya Tsukioka

We first study coupled Hirota-Iwao modified KdV (HI-mKdV) systems and give all possible local and nonlocal reductions of these systems. We then present Hirota bilinear forms of these systems and give one-soliton solutions of them with the…

Exactly Solvable and Integrable Systems · Physics 2019-11-11 Aslı Pekcan

In this study, we investigate the Klein-Gordon-Zakharov system with a focus on identifying multi-soliton solutions. Specifically, for a given number $N$ of solitons, we demonstrate the existence of a multi-soliton solution that…

Analysis of PDEs · Mathematics 2024-11-26 Vicente Alvarez , Amin Esfahani

By constructing the general six-parameter bright two-soliton solution of the integrable coupled nonlinear Schrodinger equation (Manakov model) using the Hirota method, we find that the solitons exhibit certain novel inelastic collision…

solv-int · Physics 2009-10-30 R. Radhakrishnan , M. Lakshmanan , J. Hietarinta

In this paper, we derive general bright-dark soliton solutions to the coupled Sasa-Satsuma (CSS) equation using the Kadomtsev-Petviashvili (KP) reduction method. Since the CSS equation is a special case of the four-component Hirota…

Exactly Solvable and Integrable Systems · Physics 2026-03-10 Changyan Shi , Xiyao Chen , Guangxiong Zhang , Chengfa Wu , Bao-Feng Feng

Based on the KP hierarchy reduction method, the general multi-dark soliton solutions in Gram type determinant forms for the multi-component coupled Maccari system are constructed. Especially, the three-component coupled Maccari system…

Pattern Formation and Solitons · Physics 2020-01-08 Tao Xu , Yong Chen

Higher order and multicomponent generalizations of the nonlinear Schrodinger equation are important in various applications, e.g., in optics. One of these equations, the integrable Sasa-Satsuma equation, has particularly interesting soliton…

Exactly Solvable and Integrable Systems · Physics 2009-11-10 C. Gilson , J. Hietarinta , J. Nimmo , Y. Ohta

Mixed type (bright-dark) soliton solutions of the integrable N-coupled nonlinear Schr{\"o}dinger (CNLS) equations with mixed signs of focusing and defocusing type nonlinearity coefficients are obtained by using Hirota's bilinearization…

Exactly Solvable and Integrable Systems · Physics 2015-05-13 M. Vijayajayanthi , T. Kanna , M. Lakshmanan

We show that the Yajima-Oikawa (YO) equations, a model of short wave-long wave interaction, arise from a simple geometric flow on curves in the 3-dimensional sphere $S^3$ that are transverse to the standard contact structure. For the family…

Differential Geometry · Mathematics 2024-12-18 Annalisa Calini , Thomas A. Ivey

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

The soliton solution of the integrable coupled nonlinear Schrodinger equation (NLS) of Manakov type is investigated by using Zakharov-Shabat (ZS) scheme. We get the bright N-solitons solution by solving the integrable uncoupled NLS of…

High Energy Physics - Theory · Physics 2007-05-23 Freddy P. Zen , Hendry I. Elim

In this paper, we study the novel nonlinear wave structures of a (2+1)-dimensional variable-coefficient Korteweg-de Vries (KdV) system by its analytic solutions. Its $N$-soliton solution are obtained via Hirota's bilinear method, and in…

Exactly Solvable and Integrable Systems · Physics 2024-09-27 Yaqing Liu , Linyu Peng

In this paper, we demonstrate the emergence of non-degenerate bright solitons and summarize their several interesting features in a completely integrable two-component long-wave-short-wave resonance interaction model with a general form of…

Pattern Formation and Solitons · Physics 2025-08-26 S. Stalin , M. Lakshmanan

A direct method is developed for constructing the bright $N$-soliton solution of a multi-component modified nonlinear Schr\"odinger equation. Specifically, the two different expressions of the solution are obtained both of which are…

Exactly Solvable and Integrable Systems · Physics 2015-05-30 Yoshimasa Matsuno

A space discretization of an integrable long wave-short wave interaction model, called the Yajima-Oikawa system, was proposed in the recent paper arXiv:1509.06996 using the Hirota bilinear method (see also…

Exactly Solvable and Integrable Systems · Physics 2018-09-18 Takayuki Tsuchida

We construct static solutions to a SU(2) Yang--Mills (YM) dilaton model in 4+1 dimensions subject to bi-azimuthal symmetry. The YM sector of the model consists of the usual YM term and the next higher order term of the YM hierarchy, which…

High Energy Physics - Theory · Physics 2008-11-26 Eugen Radu , Ya. Shnir , D. H. Tchrakian

There has been found an exact solution of the mixed problem for Shrodinger's compact U(m)-vector nonlinear model with an arbitrary sign of the coupling constant. It is shown, that in case of m>2 there is a new class of solutions - mixed…

Exactly Solvable and Integrable Systems · Physics 2009-11-07 A. M. Agalarov , R. M. Magomedmirzaev

A previously unknown bright N-soliton solution for an intermediate nonlinear Schr\"{o}dinger equation of focusing type is presented. This equation is constructed as a reduction of an integrable system related to a Sato equation of a…

Exactly Solvable and Integrable Systems · Physics 2007-05-23 Yohei Tutiya

In this paper, we study the formation of solitons, their propagation and collision behaviour in an integrable multicomponent (2+1)-dimensional long wave-short wave resonance interaction ($M$-LSRI) system. First, we briefly revisit our…

Pattern Formation and Solitons · Physics 2015-12-04 T Kanna , K Sakkaravarthi , M Vijayajayanthi , M Lakshmanan