(1+1)维的具有时间与空间色散的五阶方程

(1+1)dimensional fifth-order equations with temporal and spatial dispersion

研究了一个新的(1+1)维的具有时空色散可积五阶方程,推广了方程的形式,并探讨了色散关系及其各自的系数情况.利用简化Hirota方法推导了方程的可积条件,导出了多孤子解.此外,利用指数型初始解构造方程的变换,得出双线性方程,继而利用Hirota双线性导数法导出单孤子解、双孤子解及N孤子解.结合双线性方程给出了不同双线性交换算子的双线性Bäcklund变换,继而导出不同条件下的双曲行波解、周期行波解等行波解.

In this paper,a new(1+1)dimensional equation with space-time dispersion integrable fifth-order equation is studied,the form of the equation is generalized,and the dispersion relationship and its respective coefficients are discussed.The integrable conditions of the equation are derived using the simplified Hirota method,and the multi-solution is also derived.In addition,the bilinear equation is obtained using the transformation of the exponential initial solution to construct the equation,and then the Hirota bilinear derivative method is used to derive the single solitary,double solitary and N solitary solution.The bilinear equation gives the bilinear Bäcklund transform of different bilinear exchange operators,and then the hyperbolic traveling wave solution and periodic traveling wave solution are derived under different conditions.