On the extension of solutions of the real to complex KdV equation and a mechanism for the construction of rogue waves

DOI10.1080/17455030.2016.1161863zbMath1366.35155OpenAlexW2404733058MaRDI QIDQ5283125

Rabea El Shennawy Abo Elkhair, M. Tantawy, H. I. Abdel-Gawad

Publication date: 19 July 2017

Published in: Waves in Random and Complex Media (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17455030.2016.1161863

zbMATH Keywords

solitonsLie-Bäcklund symmetriesMiura and Bäcklund transformations

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40)

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Cites Work

• Towards a unified method for exact solutions of evolution equations. An application to reaction diffusion equations with finite memory transport
• Nonlocal Lie-Bäcklund symmetries of the coupled KdV system
• Multi-rogue waves for a higher-order nonlinear Schrödinger equation in optical fibers
• Physical mechanisms of the rogue wave phenomenon.
• Breathers and multi-soliton solutions for the higher-order generalized nonlinear Schrödinger equation
• The rogue wave and breather solution of the Gerdjikov-Ivanov equation
• Coupled KdV equations derived from two-layer fluids
• Exact Solution of the Korteweg—de Vries Equation for Multiple Collisions of Solitons
• Multi-rogue waves solutions: from the NLS to the KP-I equation
• Rogue waves in nonlinear Schrödinger models with variable coefficients: application to Bose-Einstein condensates

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