耦合变系数Newell-Whitehead方程的达布变换及其多孤子解

Darboux Transformation and Multi-Soliton Solutions for the Coupled Variable-Coefficient Newell-Whitehead Equation

借助耦合变系数Newell-Whitehead方程的Lax对和谱问题的规范变换构造了一个包含多参数的N-波达布变换.运用达布变换来产生耦合变系数Newell-Whitehead方程的多孤子解.变系数函数的几何和内部性质对孤波的形状和孤波的移动方向有非凡的影响.最后,通过合适地选择参数,耦合变系数Newell-Whitehead方程的多孤子解的性质被显示出来.

An N-fold Darboux transformation with multi-parameters for the coupled variable-coefficient Newell-Whitehead equation is established with the help of a gauge transformation of the spectral problem. With the application of Darboux transformation, multi-soliton solutions of the coupled variable-coefficient Newell Whitehead equation are constructed. The geometry and the internal properties of the variable coef ficient function have a remarkable influence on soliton wave shape and moving direction. Finally, the prop erties of the multi-soliton solutions of the coupled variable-coefficient Newell-Whitehead equation are ex plieitly demonstrated through appropriate parameter selection.