论文标题
完全离散的短脉冲方程的循环动力学
Loop dynamics of a fully discrete short pulse equation
论文作者
论文摘要
在本文中，将完全离散的短脉冲（SP）方程式表示为差异方程（也称为离散LAX对）的可集成性条件。此外，在连续限制下，也从完全离散的SP方程中获得了两个半差异版本的SP方程。 Darboux转换用于计算完全离散和半差异SP方程的多螺旋溶液。计算第一和第二个非平凡的孤子解决方案的明确表达式。我们还得出了完全离散的SP方程的呼吸溶液的显式表达。已经探索和说明了单回路孤子的动力学以及环路和环形 - 安列解决方案的相互作用机理。
In this article, a fully discrete short pulse (SP) equation is presented as an integrability condition of a linear system of difference equations (also known as discrete Lax pair). Additionally, two semi-discrete versions of the SP equation have also been obtained from fully discrete SP equation under continuum limits. Darboux transformation is employed to compute multi-soliton solutions of fully discrete and semi-discrete SP equations. Explicit expressions of first and second nontrivial soliton solutions are computed. We also derived explicit expression of breather solution for fully discrete SP equation. The dynamics of single loop soliton and interaction mechanism of loop-loop and loop-antiloop solutions has been explored and illustrated.
