2 + 1 KdV(N) equations

DOI10.1063/1.3629528zbMath1272.35169arXiv1102.5230OpenAlexW3105447809MaRDI QIDQ2849720

Aslı Pekcan, Metin Gürses

Publication date: 24 September 2013

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1102.5230

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Soliton solutions (35C08)

Related Items (10)

Soliton solutions of \(q\)-Toda lattice by Hirota direct method ⋮ Bäcklund transformations and soliton solutions for a \((2+1)\)-dimensional Korteweg-de Vries-type equation in water waves ⋮ A new integrable \((3+1)\)-dimensional KdV-like model with its multiple-soliton solutions ⋮ Three kinds of periodic wave solutions and their limit forms for a modified KdV-type equation ⋮ \((2+1)\)-dimensional AKNS \((-N)\) systems. II ⋮ Multi-component AKNS systems ⋮ \((2+1)\)-dimensional local and nonlocal reductions of the negative AKNS system: soliton solutions ⋮ On \((2+1)\)-dimensional mixed AKNS hierarchy ⋮ \((2+1)\)-dimensional mKdV (N) equations by the mKdV recursion operator: multiple soliton and multiple singular soliton solutions ⋮ A study on the (2 + 1)-dimensional KdV4 equation derived by using the KdV recursion operator

Cites Work

• Linear superposition principle applying to Hirota bilinear equations
• KdV6: an integrable system
• Symbolic methods to construct exact solutions of nonlinear partial differential equations
• Integrability of Kupershmidt deformations
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• PDEPtest: a package for the Painlevé test of nonlinear partial differential equations
• A search for integrable bilinear equations: The Painlevé approach
• Exact Solution of the Korteweg—de Vries Equation for Multiple Collisions of Solitons
• Nonlinearizing linear equations to integrable systems including new hierarchies with nonholonomic deformations
• Mixed hierarchy of soliton equations
• Nonholonomic deformation of KdV and mKdV equations and their symmetries, hierarchies and integrability
• Nonholonomic deformation of generalized KdV-type equations
• Extension of integrable equations
• The Painlevé property for partial differential equations
• A search for bilinear equations passing Hirota’s three-soliton condition. I. KdV-type bilinear equations
• Exact accelerating solitons in nonholonomic deformation of the KdV equation with a two-fold integrable hierarchy
• BILINEARIZATION AND SOLUTIONS OF THE KdV6 EQUATION
• A new integrable generalization of the Korteweg–de Vries equation

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