短脉冲方程的多分量推广及其多孤子解
A novel multi-component generalization of the short pulse equation and its multisoliton solutions
摘要：
我们提出了一种新的多分量非线性方程组，推广了描述超短脉冲在光纤中传输的短脉冲（SP）方程。通过双线性形式与速端图变换相结合，我们得到了其参数表示形式的多孤子解。值得注意的是，与SP方程的行列式解不同，所提出的系统被发现表现出的解决方案表示的pffeclanans。解决方案的证明是在一个基本的行列式理论的框架内进行的。简化的2组分系统值得特别考虑。特别是，我们通过建立一个拉克斯对，系统是完全可积的。详细研究了环孤子和呼吸子等解的性质，证实了它们的孤子行为。一个变种的2分量系统也讨论了其多孤子解。
英文摘要：
We propose a novel multi-component system of nonlinear equations that generalizes the short pulse (SP) equation describing the propagation of ultra-short pulses in optical fibers. By means of the bilinear formalism combined with a hodograph transformation, we obtain its multi-soliton solutions in the form of a parametric representation. Notably, unlike the determinantal solutions of the SP equation, the proposed system is found to exhibit solutions expressed in terms of pfaffians. The proof of the solutions is performed within the framework of an elementary theory of determinants. The reduced 2-component system deserves a special consideration. In particular, we show by establishing a Lax pair that the system is completely integrable. The properties of solutions such as loop solitons and breathers are investigated in detail, confirming their solitonic behavior. A variant of the 2-component system is also discussed with its multisoliton solutions.
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