非局域Gerdjikov-Ivanov方程非经典解的研究

A Study on the Non-Classical Solutions to the Non-Local Gerdjikov-Ivanov Equation

提出了非局域的Gerdjikov-Ivanov(GI)方程,利用待定系数法构造了该方程的Darboux变换,并通过选取不同的种子解,构造了该方程的亮孤子解、呼吸子解、周期波解、Kink-孤子解及双周期波解,前两种形式的解都在经典的GI方程中存在,而后几种解仅存在于非局域方程之中.因此,局域方程与非局域方程在解的结构上存在一定的差异.

In this paper,we propose the non-local Gerdjikov-Ivanov(GI)equation,and by using the method of undetermined coefficients,we construct its Darboux transformation.Then we obtain the bright soliton solutions,breather solutions,periodic wave solutions,kink-soliton solutions,and double periodic line wave solutions by choosing different seed solutions.The bright soliton solutions and the breather solutions also appear in the classical GI equation while the others are not.So the solutions to the non-local GI equation have different properties from those to the GI equation.