非线性场论方程到包络模型的约化：朝向相对论系统类似物的普遍理解
Reduction of nonlinear field theory equations to envelope models: towards a universal understanding of analogues of relativistic systems
摘要：
我们研究了一种新的映射之间的解决方案的几个成员的Klein-Gordon方程族和方程的解决方案描述其减少通过缓慢变化的包络近似。这种映射在相互作用的相对论性场的研究和更适合于实验室模拟研究的系统的研究之间建立了联系，后者由非线性薛定谔方程描述。一个新的演化方程也来自，自然出现的正弦戈登公式，具有贝塞尔函数的非线性数值研究表明，这个新的方程的解决方案包括准孤立波，呼吸器的解决方案，以及脉冲分裂和重组。
英文摘要：
We investigate a novel mapping between solutions to several members of the Klein-Gordon family of equations and solutions to equations describing their reductions via the slowly varying envelope approximation. This mapping creates a link between the study of interacting relativistic fields and that of systems more amenable to laboratory-based analogue research, the latter described by nonlinear Schrödinger equations. A new evolution equation is also derived, emerging naturally from the sine-Gordon formula, possessing a Bessel-function nonlinearity; numerical investigations show that solutions to this novel equation include quasi-solitary waves, breather solutions, along with pulse splittings and recombinations.
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