Hybrid solutions of (3 + 1)-dimensional Jimbo-Miwa equation
type: Item
instance of: scholarly article
title: Hybrid solutions of (3 + 1)-dimensional Jimbo-Miwa equation
zbMATH Open document ID: 1426.35209
DOI: 10.1155/2017/5453941
author: Yong Zhang
author: Shi-Li Sun
author: Huan-He Dong
published in: Mathematical Problems in Engineering
publication date: 2018-11-05T00:00:00Z
review text: Summary: The rational solutions, semirational solutions, and their interactions to the \((3 + 1)\)-dimensional Jimbo-Miwa equation are obtained by the Hirota bilinear method and long wave limit. The hybrid solutions contain rogue wave, lump solution, and the breather solution, in which the breathers which are manifested as growing and decaying periodic line waves show different dynamics in different planes. Rogue waves are localized in time and are obtained theoretically as a long wave limit of breathers with indefinitely larger periods; they arise from a constant background at \(t \ll 0\) and then disappear in the constant background when time goes on. More importantly, the interactions between some hybrid solutions are demonstrated in detail by the three-dimensional figures, such as hybrid solution between the stripe soliton and breather and hybrid solution between stripe soliton and lump solution.
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 35C08
Mathematics Subject Classification ID: 37K10
zbMATH DE Number: 6972222
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/5453941
OpenAlex ID: W2768575094
cites work: (2+1)-dimensional (M+N)-component AKNS system: Painlevé integrability, infinitely many symmetries, similarity reductions and exact solutions
cites work: Hamiltonian and super-Hamiltonian systems of a hierarchy of soliton equations
cites work: A family of Liouville integrable lattice equations and its conservation laws
cites work: Some reductions from a Lax integrable system and their Hamiltonian structures
cites work: A hierarchy of lattice soliton equations associated with a new discrete eigenvalue problem and Darboux transformations
cites work: Binary nonlinearization for AKNS-KN coupling system
cites work: Generalized fractional supertrace identity for Hamiltonian structure of NLS-MKdV hierarchy with self-consistent sources
cites work: The new integrable symplectic map and the symmetry of integrable nonlinear lattice equation
cites work: Bäcklund transformations and their applications
cites work: A deformed reduced semi-discrete Kaup-Newell equation, the related integrable family and Darboux transformation
cites work: Two integrable lattice hierarchies and their respective Darboux transformations
cites work: The integrability of nonisospectral and variable-coefficient KdV equation with binary Bell polynomials
cites work: Two families of Liouville integrable lattice equations
cites work: Binary Bell polynomial manipulations on the integrability of a generalized (2+1)-dimensional Korteweg-de Vries equation
cites work: A hierarchy of discrete integrable coupling system with self-consistent sources
cites work: Exact Solution of the Korteweg—de Vries Equation for Multiple Collisions of Solitons
cites work: Q4828547
cites work: Generalized bilinear differential operators, binary Bell polynomials, and exact periodic wave solution of Boiti-Leon-Manna-Pempinelli equation
cites work: Lump solutions to the Kadomtsev-Petviashvili equation
cites work: Lump solutions to dimensionally reduced \(p\)-gKP and \(p\)-gBKP equations
cites work: Lump solution of \((2+1)\)-dimensional Boussinesq equation
cites work: Rational solutions and lump solutions to the generalized \((3+1)\)-dimensional shallow water-like equation
cites work: Multi-component generalizations of the Hirota-Satsuma coupled KdV equation
cites work: Vector financial rogue waves
cites work: Financial Rogue Waves
cites work: Waves that appear from nowhere and disappear without a trace
cites work: Water waves, nonlinear Schrödinger equations and their solutions
cites work: Extreme waves that appear from nowhere: on the nature of rogue waves
cites work: Persistence of rogue waves in extended nonlinear Schrödinger equations: integrable Sasa-Satsuma case
cites work: Rational solutions to two- and one-dimensional multicomponent Yajima-Oikawa systems
cites work: Rogue wave solutions of AB system
cites work: Dynamics of Rogue Waves on a Multisoliton Background in a Vector Nonlinear Schrödinger Equation
cites work: Rogue waves in a resonant erbium-doped fiber system with higher-order effects
cites work: Solitons and infinite dimensional Lie algebras
cites work: Rogue wave and a pair of resonance stripe solitons to a reduced (3+1)-dimensional Jimbo-Miwa equation
description: scientific article; zbMATH DE number 6972222