值在Laurent级数的非阿基米德域上的泛函及其在弹性力学方程中的应用
Functionals with values in the Non-Archimedean field of Laurent series and their applications to the equations of elasticity theory
摘要：
本文将Laurent级数的非阿基米德域上的泛函应用于Hopf方程和弹性力学方程的广义解（孤子和激波形式）的定义。提出了无限窄孤子和激波的形状计算方法。应用这种方法，轮廓的计算简化为$\mathbf{R}^{n+1}$、$n>1$中的非线性代数方程组。它表明，有可能找到一些解决方案，该系统使用牛顿迭代法。被认为是例子和数值试验。
英文摘要：
Functionals with values in Non-Archimedean field of Laurent series applied to the definition of generalized solution (in the form of soliton and shock wave) of the Hopf equation and equations of elasticity theory. Calculation method for the profile of infinitely narrow soliton and shock wave is proposed. Applying this method, calculations of profiles are reduced to the nonlinear system of algebraic equations in $\mathbf{R}^{n+1}$, $n>1$. It is shown that there is a possibility to find out some of the solutions of this system using the Newton iteration method. Examples and numerical tests are considered.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
