论文标题
MKDV方程的多椭圆化解决方案及其渐近行为
The multi elliptic-localized solutions and their asymptotic behaviors for the mKdV equation
论文作者
论文摘要
我们主要在椭圆函数解决方案的背景下构建和分析用于聚焦改良的Korteweg-De Vries（MKDV）方程的多椭圆化解决方案。基于Darboux-Bäcklund变换，我们通过Jacobi Theta函数为这些溶液提供了均匀的表达。多椭圆定位溶液的渐近行为直接分为两类。通过这些溶液的一致渐近表达，我们可以获得椭圆形润呼吸器/孤子之间的碰撞是弹性的。此外，对称分析给出了孤子和呼吸器之间严格弹性碰撞的足够条件。此外，作为$ k \ rightArrow0^{+} $，多椭圆形的解决方案将其退化为孤子，呼吸器或Soliton-Breather溶液，这意味着我们将解决方案从恒定和消失的背景扩展到周期性解决方案背景。此外，我们说明了多椭圆形的解决方案的数字，以可视化上述分析。
We mainly construct and analyze the multi elliptic-localized solutions under the background of elliptic function solutions for the focusing modified Korteweg-de Vries (mKdV) equation. Based on the Darboux-Bäcklund transformation, we provide a uniform expression for these solutions by the Jacobi theta functions. The asymptotic behaviors of multi elliptic-localized solutions are provided directly in two categories. By the consistent asymptotic expression of those solutions, we obtain that the collisions between the elliptic-breathers/solitons are elastic. Moreover, a sufficient condition of the strictly elastic collision between the solitons and breathers has been given by the symmetric analysis. In addition, as $k\rightarrow0^{+}$, the multi elliptic-localized solutions degenerate into solitons, breathers or soliton-breather solutions, which implies that we extend the solutions from the constant and vanishing backgrounds to the periodic solutions backgrounds. Moreover, we illustrate figures of the multi elliptic-localized solutions to visualize the above analysis.
