微扰KdV方程中的非弹性孤子和反孤子
Inelastically generated solitons and anti-solitons in the perturbed KdV equation
摘要：
在共同扰动的作用下，KdV方程的多孤子解被转化为一个弹性分量和一个一阶非弹性分量之和。的弹性组件是一个扰动系列，在结构上相同的扰动单孤子解决方案。它保留了孤子散射的图像。非弹性分量由表示KdV孤子与非弹性产生的孤子-反孤子波之间耦合的扰动项产生。它逐渐演化为孤子和反孤子，它们沿着KdV孤子的特征线演化。这在两个孤子的情况下证明。
英文摘要：
Under the effect of common perturbations, the multiple-soliton solution of the KdV equation is transformed into a sum of an elastic and a first-order inelastic component. The elastic component is a perturbation series, identical in structure to the perturbed single-soliton solution. It preserves the soliton-scattering picture. The inelastic component is generated by perturbation terms that represent coupling between KdV solitons and inelastically generated soliton-anti-soliton waves. It asymptotes into solitons and anti-solitons, that evolve along the characteristic lines of the KdV solitons. This is demonstrated in the two-soliton case.
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。
