Alice-Bob systems, P^-T^-Ĉ symmetry invariant and symmetry breaking soliton solutions

DOI10.1063/1.5051989zbMath1395.35169OpenAlexW2889178610MaRDI QIDQ4586515

Sen-yue Lou

Publication date: 13 September 2018

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

Full work available at URL: https://doi.org/10.1063/1.5051989

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) NLS equations (nonlinear Schrödinger equations) (35Q55) Symmetry breaking in quantum theory (81R40) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Quantum coherence, entanglement, quantum correlations (81P40) Soliton solutions (35C08) Quantum information, communication, networks (quantum-theoretic aspects) (81P45)

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Cites Work

• Complete integrability and the Miura transformation of a coupled KdV equation
• Coupled KdV equations with multi-Hamiltonian structures
• Exact \(P_sT_d\) invariant and \(P_sT_d\) symmetric breaking solutions, symmetry reductions and Bäcklund transformations for an AB-KdV system
• Applications of KdV
• Integrable quartic potentials and coupled KdV equations
• Solitons and dynamics for a general integrable nonlocal coupled nonlinear Schrödinger equation
• Soliton solutions of an integrable nonlocal modified Korteweg-de Vries equation through inverse scattering transform
• Integrable multidimensional versions of the nonlocal nonlinear Schrödinger equation
• Inverse scattering transform for the integrable nonlocal nonlinear Schrödinger equation
• Integrable Nonlinear Evolution Partial Differential Equations in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>4</mml:mn><mml:mo>+</mml:mo><mml:mn>2</mml:mn></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>3</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:math>Dimensions
• Coupled KdV equations derived from two-layer fluids
• Painlevé classification of coupled Korteweg–de Vries systems
• Integrable Nonlocal Nonlinear Equations
• Towards the complete classification of homogeneous two-component integrable equations
• Solutions of Nonlocal Equations Reduced from the AKNS Hierarchy
• Davey-Stewartson type equations in 4+2 and 3+1 possessing soliton solutions

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