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 Green's function.

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.

Perturbative Influence on the Shockwave of Burgers Equation

From the point of view of evolution equations with soliton solutions,we present a general way for the study of the shockwave of one-dimensional Burgers equation under the action of perturbations.Apart from the damping case which needs a somewhat special treatment,we formulate the effects induced by other general perturbations unifyingly.

First-Order Correction of the Perturbed sine-Gordon Equation

A new direct approach based on the Fourier transformation is developed and applied to study the perturbed sine-Gordon equation.Since a new basis for perturbation expansion is introduced,the first-order correction is expressed in terms of Bessell functions.

Perturbation Theory for Optical Soliton

Based on the main idea of the derivative expansion method,a perturbation approach is proposed for the investigation of single soliton propagating down a nonideal monomode optical fiber.This approach is totally independent of inverse scattering theory,which has substantial difference from the past methods.In this scheme,the first-order correction is derived by the method of eigenfunction expansion,and the parameters change is directly obtained from the secularity conditions for some cases.

Direct Approach for Kink Solution of Ф - 4 Equation Under Perturbation

Perturbations about kink solution ofФ-4 equation are investigated by a direct approach which was recently developed in a study of soliton perturbation theory.In this scheme,the derivative expansion method from classical perturbation theory is employed to linearize the perturbed equation.The solution of the linearized equation for first-order correction is derived by the method of Laplace transformation.At the same time,the parameters variation is obtained directly from the secularity conditions.

Direct Approach Based on the Separation of Variables for the Soliton Study of Perturbed Sine-Gordon Equation

A new direct approach based on the separation of variables for the study of soliton perturbations is developed.As an example,the effects of perturbation on a soliton(kink),i.e.,both the time-dependence of soliton parameters and the first-order correction are derived for perturbed sine-Gordon equation.Our approach is very concise and easy to understand,and it can be extended directly to deal with other nonlinear evolution equations.

A Two-Soliton Solution of Cubic Schrodinger Equation

An exact two-soliton solution of cubic Schrodinger equation is derived by using the inverse scattering method,where the transmission coefficient has one pole of second order instead of two simple poles.This solution describes such a process that two infinitely separated solitons approach and then pass through each other and keep straight on infinitely.