The Lie group theoretical method is used to study the equations describing materials with competing quadratic and cubic nonlinearities. The equations shave some of the nice properties of soliton equations. From the el...The Lie group theoretical method is used to study the equations describing materials with competing quadratic and cubic nonlinearities. The equations shave some of the nice properties of soliton equations. From the elliptic functions expansion method, we obtain large families of analytical solutions, in special cases, we have the periodic, kink and solitary solutions of the equations. Furthermore, we investigate the stability of these solutions under the perturbation of amplitude noises by numerical simulation.展开更多
Lie group theoretical method and the equation of the Jacobi elliptic function are used to study the three wave system that couples two fundamental frequency （FF） and a single second harmonic （SH） one by competing...Lie group theoretical method and the equation of the Jacobi elliptic function are used to study the three wave system that couples two fundamental frequency （FF） and a single second harmonic （SH） one by competing X^（2） （quadratic） and X^（3） （cubic） nonlinearities and birefringence. This system shares some of the nice properties of soliton system. On the phase-locked condition; we obtain large families of analytical solutions as the soliton, kink and periodic solutions of this system.展开更多
We find and stabilize high-dimensional dipole and quadrupole solitons in nonlocal competing cubic-quintic nonlinear media.By adjusting the propagation constant,cubic,and quintic nonlinear coefficients,the stable inter...We find and stabilize high-dimensional dipole and quadrupole solitons in nonlocal competing cubic-quintic nonlinear media.By adjusting the propagation constant,cubic,and quintic nonlinear coefficients,the stable intervals for dipole and quadrupole solitons that are parallel to the x-axis and those after rotating 45°counterclockwise around the origin of coordinate are found.For the dipole solitons and those after rotation,their stability is controlled by the propagation constant,the coefficients of cubic and quintic nonlinearity.The stability of quadrupole solitons is controlled by the propagation constant and the coefficient of cubic nonlinearity,rather than the coefficient of quintic nonlinearity,though there is a small effect of the quintic nonlinear coefficient on the stability.Our proposal may provide a way to generate and stabilize some novel high-dimensional nonlinear modes in a nonlocal system.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos 10575087 and 10875106)
文摘The Lie group theoretical method is used to study the equations describing materials with competing quadratic and cubic nonlinearities. The equations shave some of the nice properties of soliton equations. From the elliptic functions expansion method, we obtain large families of analytical solutions, in special cases, we have the periodic, kink and solitary solutions of the equations. Furthermore, we investigate the stability of these solutions under the perturbation of amplitude noises by numerical simulation.
基金Supported by the National Natural Science Foundation of China under Grant No.10875106
文摘Lie group theoretical method and the equation of the Jacobi elliptic function are used to study the three wave system that couples two fundamental frequency （FF） and a single second harmonic （SH） one by competing X^（2） （quadratic） and X^（3） （cubic） nonlinearities and birefringence. This system shares some of the nice properties of soliton system. On the phase-locked condition; we obtain large families of analytical solutions as the soliton, kink and periodic solutions of this system.
基金supported by the National Natural Science Foundation of China(12074343,11835011)the Natural Science Foundation of the Zhejiang Province of China(LZ22A050002)。
文摘We find and stabilize high-dimensional dipole and quadrupole solitons in nonlocal competing cubic-quintic nonlinear media.By adjusting the propagation constant,cubic,and quintic nonlinear coefficients,the stable intervals for dipole and quadrupole solitons that are parallel to the x-axis and those after rotating 45°counterclockwise around the origin of coordinate are found.For the dipole solitons and those after rotation,their stability is controlled by the propagation constant,the coefficients of cubic and quintic nonlinearity.The stability of quadrupole solitons is controlled by the propagation constant and the coefficient of cubic nonlinearity,rather than the coefficient of quintic nonlinearity,though there is a small effect of the quintic nonlinear coefficient on the stability.Our proposal may provide a way to generate and stabilize some novel high-dimensional nonlinear modes in a nonlocal system.
