Re-observation on localized waves constructed by variable separation solutions of (1+1)-dimensional coupled integrable dispersionless equations via the projective Riccati equation method

DOI10.1016/j.aml.2019.04.009zbMath1435.37051OpenAlexW2940287196MaRDI QIDQ2274807

Ning Zhang, Yan Fan, Chao-Qing Dai

Publication date: 1 October 2019

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

Full work available at URL: https://doi.org/10.1016/j.aml.2019.04.009

zbMATH Keywords

singularitycoupled integrable dispersionless equationslocalized wavesprojective Riccati equation methodvariable separation exponential-form solution

Mathematics Subject Classification ID

Soliton equations (35Q51) Solutions to PDEs in closed form (35C05) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

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Cites Work

• Notes on the equivalence of different variable separation approaches for nonlinear evolution equations
• Bright and dark wirelike spatiotemporal solitons of a partially nonlocal nonlinear Schrödinger equation
• Residual symmetries, \(n\)th Bäcklund transformation and interaction solutions for (2+1)-dimensional generalized Broer-Kaup equations
• Variable-coefficient projective Riccati equation method and its application to a new (2 + 1)-dimensional simplified generalized Broer-Kaup system
• Singularity structure analysis and Hirota's bilinearisation of the coupled integrable dispersionless equations
• Rational solutions and lump solutions to the generalized \((3+1)\)-dimensional shallow water-like equation
• Diversity of interaction solutions to the \((2+1)\)-dimensional ito equation
• Lump and line soliton pairs to a \((2+1)\)-dimensional integrable Kadomtsev-Petviashvili equation
• Interactions of dromion-like structures in the \((1 + 1)\) dimension variable coefficient nonlinear Schrödinger equation
• An equation for continuous chaos
• Entire blow-up solutions for a quasilinear \(p\)-Laplacian Schrödinger equation with a non-square diffusion term
• Non-travelling wave solutions to a \((3+1)\)-dimensional potential-YTSF equation and a simplified model for reacting mixtures
• THE RELATION OF LEMNISCATE AND A LOOP SOLITON AS 3/2 AND 1 SPIN FIELDS ALONG THE MODIFIED KORTEWEG-DE VRIES EQUATION
• New Exact Solutions and Special Coherent Structures for Coupled Integrable Dispersionless Equation
• Solitons in a nonlinear model medium
• Painlevé Analysis of a New Coupled Dispersionless Equations

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