Soliton solutions to the Novikov equation and a negative flow of the Novikov hierarchy

DOI10.1016/j.aml.2018.07.036zbMath1410.35159OpenAlexW2886266059WikidataQ129425312 ScholiaQ129425312MaRDI QIDQ1726505

Xianqiang Yang

Publication date: 20 February 2019

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2018.07.036

zbMATH Keywords

soliton solutionsDarboux transformationNovikov equationreciprocal transformation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Soliton equations (35Q51) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35)

Related Items (13)

Multi-cuspon solutions of a generalized short pulse equation ⋮ Smooth multisoliton solutions of a 2-component peakon system with cubic nonlinearity ⋮ Soliton resolution and large time behavior of solutions to the Cauchy problem for the Novikov equation with a nonzero background ⋮ A new 3-component Degasperis-Procesi hierarchy ⋮ A smooth soliton solution and a periodic cuspon solution of the Novikov equation ⋮ Parametric multi-soliton solutions of a generalized Harry-Dym type equation ⋮ Multi-soliton solutions of a two-component Camassa–Holm system: Darboux transformation approach ⋮ Double Wronskian solutions to the \((2+1)\)-dimensional Broer-Kaup-Kupershmidt equation ⋮ Novikov equation: Bäcklund transformation and applications ⋮ A simple-looking relative of the Novikov, Hirota-Satsuma and Sawada-Kotera equations ⋮ A view of the peakon world through the lens of approximation theory ⋮ Darboux transformations of the Camassa-Holm type systems ⋮ Reciprocal transformations of generalized negative flows in integrable hierarchies

Cites Work

• Stability of peakons for the Novikov equation
• Explicit multipeakon solutions of Novikov's cubically nonlinear integrable Camassa-Holm type equation
• Liouville correspondences between integrable hierarchies
• Darboux transformation and multi-soliton solutions of the Camassa-Holm equation and modified Camassa-Holm equation
• Smooth multisoliton solutions and their peakon limit of Novikov’s Camassa–Holm type equation with cubic nonlinearity
• The multiple-soliton solution of the Camassa-Holm equation
• On the Camassa-Holm equation and a direct method of solution I. Bilinear form and solitary waves
• The N -soliton solution of the Degasperis–Procesi equation
• An extension of integrable peakon equations with cubic nonlinearity
• Integrable peakon equations with cubic nonlinearity
• Generalizations of the Camassa–Holm equation
• Darboux theorems and factorization of second- and third-order ordinary differential operators
• Third order spectral problems: reductions and Darboux transformations
• On the Camassa–Holm equation and a direct method of solution. II. Soliton solutions
• On the Camassa–Holm equation and a direct method of solution. III. N -soliton solutions
• The Cauchy problem for the Novikov equation

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