The robust inverse scattering method for focusing Ablowitz-Ladik equation on the non-vanishing background

DOI10.1016/j.physd.2021.132954zbMath1486.81160OpenAlexW3169710963MaRDI QIDQ2077714

Bao-Feng Feng, Yi-ren Chen, Liming Ling

Publication date: 21 February 2022

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

Full work available at URL: https://doi.org/10.1016/j.physd.2021.132954

zbMATH Keywords

Riemann-Hilbert problemDarboux transformationbreathersrogue wavesAblowitz-Ladik equationrobust inverse scattering method

Mathematics Subject Classification ID

Shock waves and blast waves in fluid mechanics (76L05) Inverse scattering problems in quantum theory (81U40) Riemann-Hilbert problems in context of PDEs (35Q15) Soliton solutions (35C08)

Related Items (11)

Robust inverse scattering method to the complex modified Korteweg-de Vries equation with nonzero background condition ⋮ Kadomtsev-Petviashvili equation: one-constraint method and lump pattern ⋮ Riemann-Hilbert problem for the focusing nonlinear Schrödinger equation with multiple high-order poles under nonzero boundary conditions ⋮ Soliton solution to the complex modified Korteweg–de Vries equation on both zero and nonzero background via the robust inverse scattering method ⋮ Nonlinear differential-difference hierarchy relevant to the Ablowitz-Ladik equation: Lax pair, conservation laws, \(N\)-fold Darboux transformation and explicit exact solutions ⋮ The discrete modified Korteweg-de Vries equation under nonzero boundary conditions ⋮ Periodic waves in the discrete mKdV equation: modulational instability and rogue waves ⋮ Bound‐state soliton and rogue wave solutions for the sixth‐order nonlinear Schrödinger equation via inverse scattering transform method ⋮ Lie symmetry analysis, exact solutions and power series solutions of the logarithmic Monge–Ampère flow evolution equation ⋮ Rogue waves on the periodic background in the complex modified KdV equation with higher-order effects ⋮ New traveling wave solutions and interesting bifurcation phenomena of generalized KdV-mKdV-like equation

Uses Software

• rogue-waves

Cites Work

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