Nonlocality and the Inverse Scattering Transform for the Pavlov Equation

DOI10.1111/sapm.12127zbMath1344.35126arXiv1507.08205OpenAlexW1665809860MaRDI QIDQ2816382

Paolo Maria Santíni, Petr G. Grinevich

Publication date: 22 August 2016

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

Full work available at URL: https://arxiv.org/abs/1507.08205

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53)

Related Items (4)

Unnamed Item ⋮ Lie symmetry analysis, optimal system, new solitary wave solutions and conservation laws of the Pavlov equation ⋮ An integral geometry lemma and its applications: the nonlocality of the Pavlov equation and a tomographic problem with opaque parabolic objects ⋮ Preface: Mark J. Ablowitz, nonlinear waves and integrable systems. Part I

Cites Work

• A class of Einstein-Weyl spaces associated to an integrable system of hydrodynamic type
• Inverse scattering problem for vector fields and the Cauchy problem for the heavenly equation
• On the integrability of \((2+1)\)-dimensional quasilinear systems
• The KPI equation with unconstrained initial data
• A hierarchy of integrable partial differential equations in \(2+1\) dimensions associated with one-parameter families of one-dimensional vector fields
• The Cauchy problem for the Pavlov equation
• On the Kadomtsev-Petviashvili Equation and Associated Constraints
• The Cauchy problem for the Kadomtsev–Petviashvili–I equation without the zero mass constraint
• Integrable hydrodynamic chains
• On the solutions of the dKP equation: the nonlinear Riemann Hilbert problem, longtime behaviour, implicit solutions and wave breaking

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