Nonlinear Fourier transforms for the sine-Gordon equation in the quarter plane

DOI10.1016/j.jde.2017.11.023zbMath1388.37074arXiv1710.01184OpenAlexW2963869942MaRDI QIDQ1688669

Lin Huang, Jonatan Lenells

Publication date: 11 January 2018

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.01184

zbMATH Keywords

sine-Gordon equationunified transform

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Scattering theory for PDEs (35P25) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15)

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Cites Work

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• Exact solutions of semiclassical non-characteristic Cauchy problems for the sine-Gordon equation
• An initial-boundary value problem for the sine-Gordon equation in laboratory coordinates
• Integrable nonlinear evolution equations on the half-line
• The sine-Gordon model and its applications. From pendula and Josephson junctions to gravity and high-energy physics
• Nonlinear Fourier Transforms and the mKdV Equation in the Quarter Plane
• The unified method: I. Nonlinearizable problems on the half-line
• A Unified Approach to Boundary Value Problems
• Method for Solving the Sine-Gordon Equation in Laboratory Coordinates
• Inverse scattering on the line
• A unified transform method for solving linear and certain nonlinear PDEs
• Method for Solving the Korteweg-deVries Equation
• Construction of solutions and asymptotics for the sine-Gordon equation in the quarter plane

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