Pan Liu-Xian

Soliton Perturbations of the Modified Korteweg de Vries Equation

The soliton perturbations of the modified Korteweg de Vries equation corresponding to different signs of the nonlinear term are studied. The first-order effects of perturbation on a soliton, namely, both the slow time-dependence of the soliton parameters and first-order corrections are derived in a direct approach based on the separation of variables.

Soliton Perturbations for a Combined KdV-MKdV Equation

The soliton perturbations for the combined Korteweg de Vries and modified Korteweg de Vries (KdV-MKdV) equation are studied. The first-order effects of perturbation on a soliton, namely both the slow time-dependence of the soliton parameters and the first-order correction are derived through constructing the appropriate Greens function.

Moving nonlinear localized modes for one-dimensional Klein-Gordon diatomic lattice

We study analytically the moving nonlinear localized vibrational modes (discrete breathers) for a one-dimensional Klein-Gordon diatomic lattice in the whole omega (q) plane of the system by means of a semi-discrete approximation, in which the carrier wave of the modes is treated explicitly while the envelope is described in the continuum approximation. We find that both pulse and kink envelope moving modes for this lattice system can occur with certain carrier wave vectors and vibrational frequencies in separate regions of the omega (q) plane. However, the kink envelope moving modes have not been reported previously for this lattice system.

A certain critical two-soliton solution of the nonlinear Schr?dinger equation

An exact two-soliton solution of the nonlinear Schrodinger equation is derived by using the Hirota direct approach. This solution describes such a critical process that two still solitons separated infinitely approach and then pass through each other and keep straight on infinitely.

Stabilizing Chaos in the rf-Driven Josephson Junction

The models of rf-driven Josephson junctions are investigated as the perturbed systems. It is shown that the heteroclinic orbits corrected by perturbations are stable if some relations between the initial constants and system parameters are satisfied, which leads to Melnikov chaos: To stabilize chaos one has to make the control parameters fitting the relations. The result is compared with the previous numerical work and a good agreement is found.

Nonlinear Gap Modes in a 1D Alternating Bond Monatomic Lattice with Anharmonicity

We analytically study the nonlinear localized gap modes in a one-dimensional atomic chain with uniform atomic mass but two periodically alternating force constants between the nearest neighbors by means of a quasi-continuum approximation. This model simulates a row of atoms in the direction of a diamond-structure type of crystals or molecular crystals with alternating double and single bonds. For this lattice system, we find that the harmonic plus quartic anharmonic terms of inter-site potential produce a new type of nonlinear localized gap modes with a slightly asymmetry distribution of atomic displacements. These localized gap modes are somewhat different from widely studied localized gap modes with a symmetry atomic displacement distribution in diatomic ion lattices.

Direct approach for soliton perturbations based on the Green's function

A direct approach has been developed for soliton perturbations based on the Greens function. We first linearized the soliton equation and then derived the Greens function corresponding to approximation equations of different orders. Finally, we obtained the effects of perturbation on a soliton, namely both the slow time dependence of the soliton parameters and the corrections up to the second-order approximation. The higher-order effects can also be obtained in the same way.

Asymmetry localized modes in an anharmonic sphalerite-structure lattice

We numerically study the intrinsic localized vibrational modes in a diatomic chain with different masses and alternating force constants between nearest neighbors. This model simulates a row of atoms in the [111] direction of sphalerite-structure crystal. We found that the harmonic and quartic anharmonic terms in the nearest-neighbor interaction potential produce the intrinsic localized modes with frequencies above the optical branch or in the gap of the linear spectrum, the distribution patterns of atom amplitudes are asymmetry with a form of quasi-even or quasi-odd-parity, and the inclusion of cubic term in the potential lowers the frequencies of the modes and introduces static displacements for the atoms.