Four-end Solutions to Elliptic Sine-gordon Equation on the Plane

The elliptic sine-Gordon equation is a semilinear elliptic PDE with a special double-well potential. It has multi-end solutions. We prove that in 4-end case, these solutions are uniquely given by the Hirota form. Moreover, we prove these solutions are L^infinity-nondegenerate and have Morse index one.

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Publication Details

Journal
Stanford Digital Repository
Published
2025-08-15
DOI
https://doi.org/10.25740/xd289kj3328
Primary Topic
Nonlinear Partial Differential Equations
Type
article
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article

Four-end Solutions to Elliptic Sine-gordon Equation on the Plane

Stanford Digital Repository
Nonlinear Partial Differential Equations
article

Four-end Solutions to Elliptic Sine-gordon Equation on the Plane

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Abstract

The elliptic sine-Gordon equation is a semilinear elliptic PDE with a special double-well potential. It has multi-end solutions. We prove that in 4-end case, these solutions are uniquely given by the Hirota form. Moreover, we prove these solutions are L^infinity-nondegenerate and have Morse index one.

Stanford Digital Repository
Stanford University (US)
Openalex Percentile: Top 45%
Nonlinear Partial Differential Equations
DOIOpen Access PDFOpenAlex
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Four-end Solutions to Elliptic Sine-gordon Equation on the Plane · Stanford Digital Repository (2025) | TGRS Research Map | TGRS