Lou S Y, Hu Heng-Chun, Tang Xiao-Yan
Department of Physics, Shanghai Jiao Tong University, China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Mar;71(3 Pt 2B):036604. doi: 10.1103/PhysRevE.71.036604. Epub 2005 Mar 11.
Exact solutions of the (n + 1)-dimensional sine-Gordon field equation are studied with help of those of the cubic nonlinear Klein-Gordon fields. The mapping relations among the sine-Gordon field equation and the cubic nonlinear Klein-Gordon fields are pure algebraic. By solving the cubic nonlinear Klein-Gordon equations, many new types of exact explicit solutions such as the periodic-periodic interaction waves, periodic-kink interaction waves, periodic perturbed "snake" shape solitary waves, etc., are displayed both analytically and graphically.
借助三次非线性克莱因 - 戈登场的精确解研究了（n + 1）维正弦 - 戈登场方程的精确解。正弦 - 戈登场方程与三次非线性克莱因 - 戈登场之间的映射关系是纯代数的。通过求解三次非线性克莱因 - 戈登方程，解析地和图形地展示了许多新型的精确显式解，如周期 - 周期相互作用波、周期 - 扭结相互作用波、周期扰动的“蛇”形孤立波等。
