Bosonization, singularity analysis, nonlocal symmetry reductions and exact solutions of supersymmetric KdV equation

DOI10.1007/JHEP05(2013)029zbMath1342.81583arXiv1308.6695MaRDI QIDQ303152

Xiao Nan Gao, Xiao-yan Tang, Sen-yue Lou

Publication date: 12 August 2016

Published in: Journal of High Energy Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1308.6695

zbMATH Keywords

integrable hierarchiessupersymmetric effective theoriesintegrable equations in physics

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Supersymmetric field theories in quantum mechanics (81T60) PDEs in connection with quantum mechanics (35Q40) Geometric theory, characteristics, transformations in context of PDEs (35A30) Solutions to PDEs in closed form (35C05)

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Cites Work

• Strings in less than one dimension and the generalized KdV hierarchies
• Super quasiperiodic wave solutions and asymptotic analysis for \(\mathcal N=1\) supersymmetric KdV-type equations
• A supersymmetric Sawada-Kotera equation
• Nonlinearization of the Lax system for AKNS hierarchy
• Superconformal field theory and SUSY \(N=1\) KdV hierarchy. II: the \(Q\)-operator
• Quantum supersymmetric Toda--mKdV hierarchies
• A supersymmetric extension of the Kadomtsev-Petviashvili hierarchy
• The bi-Hamiltonian structure of fully supersymmetric Korteweg-de Vries systems
• Deformed Heisenberg algebra, fractional spin fields, and supersymmetry without fermions
• Classical supersymmetric mechanics
• Interactions among different types of nonlinear waves described by the Kadomtsev-Petviashvili equation
• Supersymmetric integrable systems in \((2+1)\) dimensions and their Bäcklund transformation
• Darboux transformations for supersymmetric Korteweg-de Vries equations
• Hidden supersymmetry in quantum bosonic systems
• Superconformal field theory and SUSY \(N=1\) KdV hierarchy. I: Vertex operators and Yang-Baxter equation.
• Nonlinear superposition formula for \(N=1\) supersymmetric KdV equation
• Constructing the soliton solutions for theN= 1 supersymmetric KdV hierarchy
• The supersymmetric Camassa–Holm equation and geodesic flow on the superconformal group
• Nonlocal symmetries related to Bäcklund transformation and their applications
• Quasiperiodic Wave Solutions of Supersymmetric KdV Equation in Superspace
• Quantum Physics in One Dimension
• Nonlocal Symmetries for Bilinear Equations and Their Applications
• The Gardner category and nonlocal conservation laws for N=1 Super KdV
• MULTIPLE LOCAL LAGRANGIANS FOR n-COMPONENT SUPER-KORTEWEG–DE VRIES-TYPE BI-HAMILTONIAN SYSTEMS
• Supersymmetric extension of the Korteweg–de Vries equation
• A new N=2 supersymmetric Korteweg–de Vries equation
• A nonconfocal generator of involutive systems and three associated soliton hierarchies
• INTEGRABILITY AND BIHAMILTONIAN STRUCTURE OF THE EVEN ORDER SKDV HIERARCHIES
• Conformal invariance and integrable models
• Infinitely many Lax pairs and symmetry constraints of the KP equation
• Negative Kadomtsev–Petviashvili Hierarchy
• Extension of the bilinear formalism to supersymmetric KdV-type equations
• Deconstructing supersymmetry
• Non-local symmetries via Darboux transformations
• Bilinearization ofN= 1 supersymmetric Korteweg–de Vries equation revisited
• Supersymmetric extension of the scalar Born–Infeld equation
• C Neumann and Bargmann systems associated with the coupled KdV soliton hierarchy

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