Exact solution to higher-order nonlinear equations through gauge transformation

DOI10.1016/0167-2789(87)90113-8zbMath0612.76002OpenAlexW2008526867MaRDI QIDQ1088515

B. George

Publication date: 1987

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-2789(87)90113-8

zbMATH Keywords

exact solutionsLax pairsgauge transforminghierarchy of integrable higher-order nonlinear systemshighly nonlinear hydrodynamic equationinfinite sets of conserved quantitiesmixed nonlinear Schrödinger equationStokes instability

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Degenerate parabolic equations (35K65) Navier-Stokes equations (35Q30) Schrödinger operator, Schrödinger equation (35J10) Foundations of fluid mechanics (76A02)

Related Items (43)

The inviscid limit of the derivative complex Ginzburg-Landau equation ⋮ Hierarchies and Hamiltonian structures of the nonlinear Schrödinger family using geometric and spectral techniques ⋮ Madelung fluid description on a generalized mixed nonlinear Schrödinger equation ⋮ \(N\)-soliton solution of the Kundu-type equation via Riemann-Hilbert approach ⋮ Envelope bright- and dark-soliton solutions for the Gerdjikov-Ivanov model ⋮ Soliton behavior for a generalized mixed nonlinear Schrödinger model with N-fold Darboux transformation ⋮ Interactions of localized wave and dynamics analysis in generalized derivative nonlinear Schrödinger equation ⋮ Three different methods for new soliton solutions of the generalized NLS equation ⋮ Multi-component generalized Gerdjikov-Ivanov integrable hierarchy and its Riemann-Hilbert problem ⋮ Long-time asymptotics for a mixed nonlinear Schrödinger equation with the Schwartz initial data ⋮ On integrable wave interactions and Lax pairs on symmetric spaces ⋮ The Korteweg capillarity system. Integrable reduction via gauge and reciprocal links ⋮ Analysis of fractional Kundu-Eckhaus and massive Thirring equations using a hybridization scheme ⋮ The Riemann-Hilbert approach for the higher-order Gerdjikov-Ivanov equation, soliton interactions and position shift ⋮ Inverse scattering transform for the Gerdjikov-Ivanov equation with nonzero boundary conditions ⋮ Solitonic interactions, Darboux transformation and double Wronskian solutions for a variable-coefficient derivative nonlinear Schrödinger equation in the inhomogeneous plasmas ⋮ Modulation of nonlinear waves near the marginal state of instability in fluid-filled elastic tubes. ⋮ Extended auxiliary equation method and its applications to three generalized NLS equations ⋮ Kinky breathers, multi-peak and multi-wave soliton solutions for the nonlinear propagation of Kundu–Eckhaus dynamical model ⋮ Integrable evolution systems based on Gerdjikov–Ivanov equations, bi-Hamiltonian structure, finite-dimensional integrable systems and N-fold Darboux transformation ⋮ Modulation instability, higher-order rogue waves and dynamics of the Gerdjikov-Ivanov equation ⋮ Dynamics of the higher-order rogue waves for a generalized mixed nonlinear Schrödinger model ⋮ Darboux transformation and soliton-like solutions of nonlinear Schrödinger equations ⋮ A family of completely integrable multi-Hamiltonian systems explicitly related to some celebrated equations ⋮ Variable separation and algebro-geometric solutions of the Gerdjikov-Ivanov equation ⋮ Uniformly constructing finite-band solutions for a family of derivative nonlinear Schrödinger equations ⋮ The derivative nonlinear Schrödinger equation with zero/nonzero boundary conditions: inverse scattering transforms and \(N\)-double-pole solutions ⋮ Bifurcations and new exact travelling wave solutions for the Gerdjikov-Ivanov equation ⋮ Multi-component Gerdjikov-Ivanov system and its Riemann-Hilbert problem under zero boundary conditions ⋮ Pseudo-spectral solution of nonlinear Schrödinger equations ⋮ Trace formula and new form of \(N\)-soliton to the Gerdjikov-Ivanov equation ⋮ CONSTRUCTING 2N-SOLITON PERIODIC WAVE SOLUTIONS FOR GENERALIZED DERIVATIVE NONLINEAR SCHRÖDINGER EQUATION ⋮ Inverse scattering transform and multiple high-order pole solutions for the Gerdjikov-Ivanov equation under the zero/nonzero background ⋮ PINN deep learning method for the Chen-Lee-Liu equation: rogue wave on the periodic background ⋮ \(N\)-soliton solutions to the multi-component nonlocal Gerdjikov-Ivanov equation via Riemann-Hilbert problem with zero boundary conditions ⋮ Exact solutions of the Gerdjikov-Ivanov equation using Darboux transformations ⋮ Riemann-Hilbert method and N-soliton for two-component Gerdjikov-Ivanov equation ⋮ Modulational instability, interactions of localized wave structures and dynamics in the modified self-steepening nonlinear Schrödinger equation ⋮ Solutions of 1+1 relativistic field models ⋮ Bright and dark solitons and periodic wave solutions for the Gerdjikov-Ivanov equation in nonlinear fiber optics ⋮ A new form of general soliton solutions and multiple zeros solutions for a higher-order Kaup–Newell equation ⋮ Darboux transformation and Rogue waves of the Kundu-nonlinear Schrödinger equation ⋮ Riemann-Hilbert approach to the modified nonlinear Schrödinger equation with non-vanishing asymptotic boundary conditions

Cites Work

• Unnamed Item
• On sigma-models with noncompact groups
• Integrable Hamiltonian systems and interactions through quadratic constraints
• Exact Solutions of the Derivative Nonlinear Schrödinger Equation under the Nonvanishing Conditions
• A Generalization of Inverse Scattering Method
• A General Theory for Interactions Between Short and Long Waves
• On the modulation of water waves in the neighbourhood of kh ≈ 1.363
• Integrability of Nonlinear Hamiltonian Systems by Inverse Scattering Method
• Topics on Solitons in Plasmas

This page was built for publication: Exact solution to higher-order nonlinear equations through gauge transformation