经典非线性场的1+1维可分性
Separability in 1+1 Dimensions in Classical Nonlinear Fields
摘要：
非线性方程的孤波解和孤子解是物理学家熟知的。孤立子是一种孤立波，它具有一些突出的特性，这些特性使得它在非线性系统中的研究成为可能。事实上，大多数有孤波解的非线性系统都没有孤波解。要使孤立波成为孤立子，我们必须准备一些初始条件，使两个或多个孤立波解碰撞。事实上，对于任何具有孤立波解的非线性系统，都不可能准备这样的初始条件。本文研究了一个系统所应具备的条件，以准备其单孤波解的组合作为碰撞的初始条件。这些系统接受分离的单个孤立波的组合作为初始条件，因此我们称它们为可分离系统。我们看到一个具有周期势的系统，零是它的真空点之一，是可分的。我们观察到可分系统有两个不同的孤子集，但一般来说，如果我们碰撞不同集合的成员，他们可能不会表现得像孤子。
英文摘要：
Solitary wave and soliton solutions of nonlinear equations are well known for physicists. A soliton is a solitary wave with some outstanding features which make it reasonable to be studied seriously in nonlinear systems. In fact most of the nonlinear systems which have solitary wave solutions, has no soliton solutions. To realize a solitary wave as a soliton, we must prepare some initial conditions to collide two or more solitary wave solutions. In fact it is not possible to prepare such initial conditions for any nonlinear system with solitary wave solutions. In this paper we study the conditions that a system should have, to prepare a combination of its single solitary wave solutions as an initial condition for collision. These systems accept a combination of separated single solitary waves as an initial condition, so we call them separable systems. We see a system with periodic potential that zero is one of its vacuum points is separable. We observed that separable systems have two distinct set of solitons, but in general, if we collide members of different sets, they may not behave like solitons.
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。
