Variable-coefficient KdV Equation Research Articles

CONSERVATION LAWS OF THE VARIABLE COEFFICIENT KdV AND MKdV EQUATIONS

In this paper, by using the Miura's method, we study the infinite conservation laws of the variable coefficient KdV and MKdV equations with three arbitrary functions of t. The result points out that the conserved densities which have the structures completely similar to the con-stat coefficient KdV and MKdV equations depend only on one arbitrary function. The other two arbitrary functions are contained only in the corresponding fluxes.

Improving accident investigation at two case companies: Evaluation of results

In this study, the generalized modified variable-coefficient KdV equation with external-force term (gvcmKdV) describing atmospheric blocking located in the mid-high latitudes over ocean is studied for integrability property by using consistent Riccati expansion solvability and the necessary integrability conditions between the function coefficients are obtained. Moreover, several new solutions have been constructed for the gvcmKdV. Additionally, the classical direct similarity reduction method is used to reduce the gvcmKdV to a nonlinear ordinary differential equation. Building on the solutions given in the previous literature for the reduced equation, many novel solitary and periodic wave solutions have been obtained for the gvcmKdV.

The inverse scattering transforms for certain types of variable coefficient KdV equations

In this paper we extend the method given by Zakharov and Shabat to a more general case. As a result it becomes possible to construct inverse scattering transforms for the class of variable coefficient KdV equations which are directly integrable. Two special cases are discussed.

Unified theory of static, dynamic, and electronic properties of aluminium

Although their coefficient functions often make the studies very hard, the variable-coefficient nonlinear evolution equations (vcNLEEs) are of current interests since they are able to model the real world in many fields of physical and engineering sciences. In this paper, based on the computerized symbolic computation, a variable-coefficient balancing-act method is proposed. Being concise and straightforward, it can be applicable to certain vcNLEEs, to get the solitonic features out, along with other exact analytic solutions, all beyond the travelling waves. By virtue of the method, such new solutions are demonstrated for a variable-coefficient KdV equation arising from fluid dynamics, plasmas and other fields. Special attention is paid to the one- and two-soliton-type solutions. Sample applications and physical interests are discussed, such as coastal waters of the world oceans, plasma physics, liquid drops and bubbles. Nonlinear interaction hallmarked by the phase shifts is pictured. Comparisons are made with other results in the literature.