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The nonlinear Schrodinger equation is proved to be consistent-tanh-expansion (CTE) solvable. Some types of dark soliton solutions dressed by cnoidal periodic waves are obtained by means of the CTE method. 相似文献
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Based on the invariant expansion method,some reasonable approximate solutions of coupled Korteweg-de Vries(KdV)equations with diferent linear dispersion relations have been obtained.These solutions contain not only bell type soliton solutions but also periodic wave solutions that expressed by Jacobi elliptic functions.The results also show that if the arbitrary constants are selected suitably,the approximate solutions may become the exact ones. 相似文献
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Riccati-type Bcklund transformations of nonisospectral and generalized variable-coefficient KdV equations 下载免费PDF全文
We extend the method of constructing Bcklund transformations for integrable equations through Riccati equations to the nonisospectral and the variable-coefficient equations. By taking nonisospectral and generalized variable-coefficient Korteweg–de Vries(KdV) equations as examples, their B¨acklund transformations are obtained under a more generalized constrain condition. In addition, the Lax pairs and infinite numbers of conservation laws of these equations are given. Especially, some classical equations such as the cylindrical KdV equation are just the special cases of the constrain condition. 相似文献
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So far, Lou's direct perturbation method has been applied
successfully to solve the nonlinear Schr?dinger equation(NLSE)
hierarchy, such as the NLSE, the coupled NLSE, the critical NLSE,
and the derivative NLSE. But to our knowledge, this method for
other types of perturbed nonlinear evolution equations has still
been lacking. In this paper, Lou's direct perturbation method is
applied to the study of perturbed complex Burgers equation. By this
method, we calculate not only the zero-order adiabatic solution,
but also the first order modification. 相似文献
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In this paper Lou's direct perturbation method is applied to the perturbed coupled nonlinear Schrodinger equations to obtain their asymptotical solutions, which include not only the zero-order solutions but also the first-order modifications. Based on the asymptotical solutions, the effects of perturbations on soliton parameters and the collision between two solitons are then discussed in brief. Furthermore, we directly simulate the perturbed coupled nonlinear SchrSdinger equations by split-step Fourier method to check the validity of the direct perturbation method. It turns out that our analytical results are well supported by the numerical calculations. 相似文献