When a one-dimensional nonlinear evolution equation could be transformed into a bilinear differential form as F（Dt, Dx）f . f = O, Hirota proposed a condition for the above evolution equation to have arbitrary N-soli...When a one-dimensional nonlinear evolution equation could be transformed into a bilinear differential form as F（Dt, Dx）f . f = O, Hirota proposed a condition for the above evolution equation to have arbitrary N-soliton solutions, we call it the 1-dimensional Hirota condition. As far as higher-dimensional nonlinear evolution equations go, a similar condition is established in this paper, also we call it a higher-dimensional Hirota condition, a corresponding judging theory is given. As its applications, a few two-dimensional KdV-type equations possessing arbitrary N-soliton solutions are obtained.展开更多
基金The project supported by National Natural Science Foundation of China under Grant No.10471139
文摘When a one-dimensional nonlinear evolution equation could be transformed into a bilinear differential form as F（Dt, Dx）f . f = O, Hirota proposed a condition for the above evolution equation to have arbitrary N-soliton solutions, we call it the 1-dimensional Hirota condition. As far as higher-dimensional nonlinear evolution equations go, a similar condition is established in this paper, also we call it a higher-dimensional Hirota condition, a corresponding judging theory is given. As its applications, a few two-dimensional KdV-type equations possessing arbitrary N-soliton solutions are obtained.
