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Related papers: Soliton Resonances for MKP-II

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The study of nonlocal nonlinear systems and their dynamics is a rapidly increasing field of research. In this study, we take a closer look at the extended nonlocal Kadomtsev-Petviashvili (enKP) model through a systematic analysis of…

Pattern Formation and Solitons · Physics 2023-08-21 K. Sakkaravarthi , Sudhir Singh , N. Karjanto

Physically relevant soliton solutions of the resonant nonlinear Schrodinger (RNLS) equation with nontrivial boundary conditions, recently proposed for description of uniaxial waves in a cold collisionless plasma, are considered in the…

Exactly Solvable and Integrable Systems · Physics 2009-11-11 Jyh-Hao Lee , Oktay K. Pashaev

We study a complex non-newtonian fluid that models the flow of nematic liquid crystals. The fluid is described by a system that couples a forced Navier-Stokes system with a parabolic-type system. We prove the existence of global weak…

Analysis of PDEs · Mathematics 2015-05-14 Marius Paicu , Arghir Zarnescu

Bright plane soliton solutions of an integrable (2+1) dimensional ($n+1$)-wave system are obtained by applying Hirota's bilinearization method. First, the soliton solutions of a 3-wave system consisting of two short wave components and one…

Exactly Solvable and Integrable Systems · Physics 2009-11-13 T. Kanna , M. Vijayajayanthi , K. Sakkaravarthi , M. Lakshmanan

This article is a brief review of the results of studying the collapse of sound waves in media with positive dispersion, which is described in terms of the three-dimensional Kadomtsev-Petviashvili (KP) equation. The KP instability of…

Pattern Formation and Solitons · Physics 2022-09-07 E. A. Kuznetsov

By virtue of the KP hierarchy reduction technique, we construct the general bright-dark mixed $N$-soliton solution to the multi-component Mel'nikov system comprised of multiple (say $M$) short-wave components and one long-wave component…

Exactly Solvable and Integrable Systems · Physics 2017-09-13 Zhong Han , Yong Chen

We consider a general multicomponent (2+1)-dimensional long-wave--short-wave resonance interaction (LSRI) system with arbitrary nonlinearity coefficients, which describes the nonlinear resonance interaction of multiple short waves with a…

Exactly Solvable and Integrable Systems · Physics 2014-12-11 K. Sakkaravarthi , T. Kanna , M. Vijayajayanthi , M. Lakshmanan

The novel generalized perturbation (n, M)-fold Darboux transformations (DTs) are reported for the (2+1)-dimensional Kadomtsev-Petviashvili (KP) equation and its extension by using the Taylor expansion of the Darboux matrix. The generalized…

Pattern Formation and Solitons · Physics 2016-12-07 Xiao-Yong Wen , Zhenya Yan

A general form of $N$-dark soliton solutions of the multi-component Mel'nikov system is presented. Taking the coupled Mel'nikov system comprised of two-component short waves and one-component long wave as an example, its general…

Pattern Formation and Solitons · Physics 2017-08-02 Zhon Han , Yong Chen , Junchao Chen

In this work, by using the Hirota bilinear method, we obtain one- and two-soliton solutions of integrable $(2+1)$-dimensional $3$-component Maccari system which is used as a model describing isolated waves localized in a very small part of…

Exactly Solvable and Integrable Systems · Physics 2021-02-03 Aslı Pekcan

The purpose of this paper is to expand the recent work of Sardar et al. [Phys. Plasmas 23, 123706 (2016)] on the existence and stability of alternative dust ion acoustic solitary wave solution of the combined modified Kadomtsev Petviashvili…

Plasma Physics · Physics 2018-10-16 Sankirtan Sardar , Anup Bandyopadhyay , K. P. Das

The aim of this paper is to apply Hirota's bilinear method to the integrable discrete Manakov system in the focusing dispersion regime in order to construct and analyze soliton and breather solutions. After deriving the general bilinear…

Exactly Solvable and Integrable Systems · Physics 2026-05-26 Uyen Le , Alexander Chernyavsky , Barbara Prinari

The stem structure is a localized feature that arises during high-order soliton interactions, connecting the vertices of two V-shaped waveforms. The interaction of resonant 3-solitons is accompanied by soliton reconnection phenomena,…

Mathematical Physics · Physics 2026-01-29 Feng Yuan , Jingsong He , Yi Cheng

In nonlinear physics, the interactions among solitons are well studied thanks to the multiple soliton solutions can be obtained by various effective methods. However, it is very difficult to study interactions among different types of…

Exactly Solvable and Integrable Systems · Physics 2012-08-17 Xue-Ping Cheng , Chun-Li Chen , Sen-Yue Lou

The celebrated (1+1)-dimensional Korteweg de-Vries (KdV) equation and its (2+1)-dimensional extention, the Kadomtsev-Petviashvili (KP) equation, are two of the most important models in physical science. The KP hierarchy is explicitly…

Exactly Solvable and Integrable Systems · Physics 2020-08-26 S. Y. Lou

We study a two-dimensional incoherently pumped exciton-polariton condensate described by an open-dissipative Gross-Pitaevskii equation for the polariton dynamics coupled to a rate equation for the exciton density. Adopting a hydrodynamic…

The generalized hierarchies of compound WKI-SP (Wadati-Konno-Ichikawa and short pulse) equations are presented. The proposed integrable nonlinear equations include the WKI-type equations, the SP-type equations and the compound generalized…

Exactly Solvable and Integrable Systems · Physics 2023-05-05 Xiaorui Hu , Tianle Xu , Junyang Zhang , Shoufeng Shen

Whitham modulation theory for certain two-dimensional evolution equations of Kadomtsev-Petviashvili (KP) type is presented. Three specific examples are considered in detail: the KP equation, the two-dimensional Benjamin-Ono (2DBO) equation…

Pattern Formation and Solitons · Physics 2018-07-19 Mark J. Ablowitz , Gino Biondini , Igor Rumanov

The current work investigates the soliton solutions of the Kaup-Boussinesq equation using the Inverse Scattering Transform method. We outline the construction of the Riemann-Hilbert problem for a pair energy-dependent spectral problems for…

Mathematical Physics · Physics 2017-05-16 Jack Haberlin , Tony Lyons

In the present paper, we are concerned with the tau function and its connection with the Kadomtsev-Petviashvili (KP) theory for the massive Thirring (MT) model. First, we bilinearize the massive Thirring model under both the vanishing and…

Exactly Solvable and Integrable Systems · Physics 2021-11-11 Junchao Chen , Bao-Feng Feng