Symplectic computation of solitary waves for general sine-Gordon equations
The paper presents a class of symplectic schemes for the numerical computation of the solutions of the sine-Gordon equation: NEWLINE\[NEWLINE\partial_t^2u- \partial_x^2u+ g(u)= 0, \qquad (x,t)\in \mathbb{R}\times (0,\infty).NEWLINE\]NEWLINE It is demonstrated that these schemes preserve the long-time global structure and the topological stabilities of solitary waves. Numerical experiments show that such symplectic schemes are suitable tools for the numerical computation and investigation of the global geometric structure for the solution of general sine-Gordon type systems, reproducing most of the structure of interest.
scientific article; zbMATH DE number 1619793
scientific article