A novel approach for solving the three-dimensional sine-Gordon equation
Sergey G Artyshev
TL;DR
This paper introduces a new analytical method for solving the three-dimensional sine-Gordon equation by leveraging its relation to the three-dimensional wave equation, providing explicit solutions and demonstrating the approach.
Contribution
It presents a novel analytical approach connecting solutions of the wave and sine-Gordon equations in three dimensions, expanding solution techniques for nonlinear PDEs.
Findings
Derived explicit solutions for the 3D sine-Gordon equation
Established a relation between wave and sine-Gordon solutions in 3D
Demonstrated the method with example solutions
Abstract
A new way for finding analytical solutions of the three-dimensional sine-Gordon equation is presented. The method is based on the established relation between the solutions of the three-dimensional wave equation and solutions of the three-dimensional sine-Gordon equation. Some examples of the solutions thus obtained are show.
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Taxonomy
TopicsAdvanced Fiber Optic Sensors · Nonlinear Waves and Solitons