形变映射法在求解非线性Klein-Gordon方程中的应用——以Φ4方程和Φ6方程为例
PDF下载 (237)贾 曼.形变映射法在求解非线性Klein-Gordon方程中的应用——以Φ4方程和Φ6方程为例[J].宁波大学学报(理工版),2020,33(5):56-61.DOI:
JIA Man.Application of deformation relations in solving nonlinear Klein-Gordon field models[J].Journal of Ningbo University(Natural Science & Engineering Edition),2020,33(5):56-61.DOI:
| Title: | Application of deformation relations in solving nonlinear Klein-Gordon field models |
| 作者: | 贾 曼 |
| Author(s): | JIA Man |
| 关键词: | 形变映射; 非线性Klein-Gordon方程; ?4方程; Φ6方程; 贝克隆变换; 非线性叠加; ϕ4 field model; Φ6 equation; Bäcklund transformation |
| Keywords: | deformation relations; nonlinear Klein-Gordon equation; nonlinear superpositions |
| 分类号: | O415 |
| 文献标识码: | A |
| 摘要: | 非线性Klein-Gordon方程在场论中具有十分重要的物理意义, 且通常是不可积的. 形变映射法利用场论中可积场方程的已知孤子解、周期解等共同特征, 通过建立一般特解间的联系来求解不可积场的新解析解. 形变映射法可以将一个非线性系统的某些重要的严格解和其他系统互相联系起来, 从而得到这些非线性系统的新类型严格解, 例如多个椭圆周期波的相互作用解或椭圆周期波和孤立波的相互作用解; 也可以利用系统自身的形变映射关系, 得到同一个系统不同解之间的形变映射关系, 从而得到系统的新严格解. 将严格解映射到系统自身, 就是系统的贝克隆变换. |
| Abstract: | The nonlinear Klein-Gordon equations play an important role in field theory and are usually considered non-integrable. Based on the common characters of the known soliton solutions and periodic solutions to the intergrable equations in field theory, deformation mapping method is constructed to find the new exact solutions of the non-intergrable equations. Deformation mapping method connects some important exact solutions of a nonlinear system to those of the other nonlinear systems, thus the new type solutions of those systems can be found, such as the conoidal periodic-periodic interaction waves and periodic-solitary interaction waves. The mapping relations also connect different exact solutions of a system so that new exact solutions to the same system are constructed. By transforming the old solutions to the new solutions of the same system, the deformation mapping relations become the B?cklund transformations of the system. |
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| 备注/Memo: | 收稿日期: 2020－05－11. 宁波大学学报（理工版）网址: http://journallg.nbu.edu.cn/ 基金项目: 国家自然科学基金（11675084）; 宁波市自然科学基金（2015A610159）; 宁波大学王宽诚幸福基金. 作者简介: 贾曼（1979－）, 女, 河北唐山人, 博士/副教授, 主要研究方向: 非线性物理. E-mail: jiaman@nbu.edu.cn 宁波大学学报（理工版）网址：http://journallg.nbu.edu.cn/ |
