Painlevé analysis of nonlinear evolution equations -- an algorithmic method

DOI10.1016/j.chaos.2005.02.043zbMath1088.35553OpenAlexW2163640360MaRDI QIDQ813524

N. E. Zubov

Publication date: 13 February 2006

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.chaos.2005.02.043

zbMATH Keywords

integrabilitynonlinear Schrödinger equationLax pairLax complexPainlevé expansionsvector Manakov system

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton equations (35Q51)

Related Items

Solitary waves for a nonlinear dispersive long wave equation, CRE solvability and soliton-cnoidal wave interaction solutions of the dissipative \((2+1)\)-dimensional AKNS equation, Multiple-mode wave solutions in Vakhnenko equation, A generalized \((\frac{G'}{G})\)-expansion method and its applications, Combining dither smoothing technique and state feedback linearization to control undifferentiable chaotic systems, Symbolic computation of exact solutions for the compound KdV-Sawada–Kotera equation

Cites Work

• The Estabrook-Wahlquist method with examples of application
• A unified approach to Painlevé expansions
• Monodromy- and spectrum-preserving deformations. I
• Linearity inside nonlinearity: Exact solutions to the complex Ginzburg-Landau equation
• Relationships among Inverse Method, Backlund Transformation and an Infinite Number of Conservation Laws
• A new truncation in Painleve analysis
• Unified approach to Miura, Bäcklund and Darboux Transformations for Nonlinear Partial Differential Equations
• The two-singular-manifold method: I. Modified Korteweg-de Vries and sine-Gordon equations
• The two-singular manifold method: II. Classical Boussinesq system
• The singular manifold method revisited
• Painleve analysis and integrability of coupled non-linear Schrodinger equations
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item