Theory of boundary effects on sine‐Gordon solitons
作者:
R. M. DeLeonardis,
S. E. Trullinger,
R. F. Wallis,
期刊:
Journal of Applied Physics
(AIP Available online 1980)
卷期:
Volume 51,
issue 2
页码: 1211-1226
ISSN:0021-8979
年代: 1980
DOI:10.1063/1.327690
出版商: AIP
数据来源: AIP
摘要:
We examine the properties of solutions to the sine‐Gordon equation in the presence of various boundary conditions. Reflection from the boundary of a semi‐infinite system with a fixed or free endpoint is found to be explainable in terms of the standard soliton‐soliton and soliton‐antisoliton solutions, respectively, for the infinite system. We also consider both nonlinear standing‐wave and solitonic solutions to the sine‐Gordon equation on a system of finite lengthL. Through the use of the application by Costabileetal. of the separation of variables ansatz due to Lamb, analytic expressions in terms of Jacobi elliptic functions are found for these two types of solutions, which assume the forms appropriate to the infinite and semi‐infinite system, respectively, asL→∞. Concentrating on the solitonic solution, we examine its symmetry properties, relations among its characteristic parameters, and give plots of its waveform in several cases. The effect of the boundaries on this solution is such that the oscillation of the soliton center closely resembles that of a particle in a symmetric potential, whose shape is determined straightforwardly from the time dependence of the soliton position and of the potential energy of the system.
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