Rational solutions for a (3+1)-dimensional nonlinear evolution equation

DOI10.1016/j.cnsns.2019.105116zbMath1450.35242OpenAlexW2991635114WikidataQ126806918 ScholiaQ126806918MaRDI QIDQ2207798

Xin Wang, Jiao Wei, Xiangguo Geng

Publication date: 23 October 2020

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2019.105116

zbMATH Keywords

Darboux transformationrational solutionrogue wave(3+1)-dimensional nonlinear evolution equationlump solution

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) NLS equations (nonlinear Schrödinger equations) (35Q55) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Soliton solutions (35C08)

Related Items

Riemann-Hilbert approach and long-time asymptotics for the three-component derivative nonlinear Schrödinger equation ⋮ A vector Geng-Li model: new nonlinear phenomena and breathers on periodic background waves ⋮ New solitons and multishock wave structures for the conformable space fractional Burger and time fractional Sharma-Tasso-Olver models ⋮ The nth-Darboux transformation and explicit solutions of the PT-symmetry second-type derivative nonlinear Schrödinger equation ⋮ An optimal system of Lie subalgebras and group-invariant solutions with conserved currents of a \((3+1)\)-D fifth-order nonlinear model I with applications in electrical electronics, chemical engineering and pharmacy ⋮ A new approach to investigate the nonlinear dynamics in a \((3 + 1)\)-dimensional nonlinear evolution equation via Wronskian condition with a free function ⋮ Antidark solitons and soliton molecules in a \((3 + 1)\)-dimensional nonlinear evolution equation ⋮ Integrability, Darboux transformation and exact solutions for nonlocal couplings of AKNS equations ⋮ Two synthetical five-component nonlinear integrable systems: Darboux transformations and applications ⋮ Analytical treatment of the generalized Hirota-Satsuma-Ito equation arising in shallow water wave ⋮ Dynamics of transformed nonlinear waves in the (3+1)-dimensional B-type Kadomtsev-Petviashvili equation. I: Transitions mechanisms ⋮ Lump and lump-soliton interaction solutions for an integrable variable coefficient Kadomtsev–Petviashvili equation ⋮ Dark-dark solitons, soliton molecules and elastic collisions in the mixed three-level coupled Maxwell-Bloch equations ⋮ Dynamical soliton wave structures of one-dimensional Lie subalgebras via group-invariant solutions of a higher-dimensional soliton equation with various applications in ocean physics and mechatronics engineering

Cites Work

• Unnamed Item
• Quasi-periodic solutions to the hierarchy of four-component Toda lattices
• Consistent Riccati expansion solvability and soliton-cnoidal wave interaction solution of a \((2 + 1)\)-dimensional Korteweg-de Vries equation
• Rogue waves and rational solutions of a \((3+1)\)-dimensional nonlinear evolution equation
• Darboux transformation and rogue wave solutions for the variable-coefficients coupled Hirota equations
• Waves that appear from nowhere and disappear without a trace
• \(N\)-soliton solution and its Wronskian form of a \((3+1)\)-dimensional nonlinear evolution equation
• Physical mechanisms of the rogue wave phenomenon.
• Nonlocal symmetry, CRE solvability and soliton-cnoidal solutions of the \((2+1)\)-dimensional modified KdV-Calogero-Bogoyavlenkskii-Schiff equation
• New integrable (\(3+1\))-dimensional systems and contact geometry
• Three-wave resonant interactions: multi-dark-dark-dark solitons, breathers, rogue waves, and their interactions and dynamics
• The nonlinear steepest descent method to long-time asymptotics of the coupled nonlinear Schrödinger equation
• Nonlinear waves in the modulation instability regime for the fifth-order nonlinear Schrödinger equation
• Darboux transformation and nonautonomous solitons for a modified Kadomtsev-Petviashvili equation with variable coefficients
• Rogue waves of a \((3+1)\)-dimensional nonlinear evolution equation
• Rogue wave and a pair of resonance stripe solitons to a reduced (3+1)-dimensional Jimbo-Miwa equation
• Darboux transformation of the coupled nonisospectral Gross-Pitaevskii system and its multi-component generalization
• Periodic and rational solutions of the reduced Maxwell-Bloch equations
• Nonautonomous characteristics of lump solutions for a \((2 + 1)\)-dimensional Korteweg-de Vries equation with variable coefficients
• Evolution of initial discontinuity for the defocusing complex modified KdV equation
• Baseband modulation instability, rogue waves and state transitions in a deformed Fokas-Lenells equation
• Lump solutions to the Kadomtsev-Petviashvili equation
• High-order rogue waves for the Hirota equation
• Darboux transformations in integrable systems. Theory and their applications to geometry
• The rogue wave and breather solution of the Gerdjikov-Ivanov equation
• Water waves, nonlinear Schrödinger equations and their solutions
• Algebraic-geometrical solutions of some multidimensional nonlinear evolution equations
• The Riemann theta function solutions for the hierarchy of Bogoyavlensky lattices
• Rogue Waves for an Alternative System of Coupled Hirota Equations: Structural Robustness and Modulation Instabilities
• Rogue waves and W-shaped solitons in the multiple self-induced transparency system
• Dynamics of rogue waves in the Davey–Stewartson II equation
• A Pair of Resonance Stripe Solitons and Lump Solutions to a Reduced (3+1)-Dimensional Nonlinear Evolution Equation
• Modelling rogue waves through exact dynamical lump soliton controlled by ocean currents
• Multi-rogue waves solutions: from the NLS to the KP-I equation