In this paper, we apply the Miura transformation to construct the connection between a variablecoefficient KdV (vcKdV) equation and a variable-coefficient modified KdV (vcmKdV) equation under certain constraint. Solving the vcmKdV equation by use of the auxiliary equation method and using the Miura transformation, we find a rich variety of new exact solutions for the vcKdV equation, which inclu...

|||||||||||||||||||||||||||||||Abstract In this paper, the researcher proposes a modi ed new method to rank L-R fuzzy numbers. The modi ed method uses a defuzzi cation of parametrically represented fuzzy numbers that have been studied in [20]. This parameterized defuzzi cation can be used as a crisp approximation with respect to a fuzzy quantity. In this article, the researcher uses this defuzz...

In this article, we discuss wavelet versions of nonparametric curve estimators and weighted least squares wavelet regression. We introduce a modi ̄ed wavelet version of the Gasser-MÄ uller estimator that is unbiased whenever a wavelet representation of the nonparametric response curve correctly speci ̄es the response. In some cases, involving the Daubechies wavelet system, we ̄nd that the modi ̄ed ...

Recent concept of integrable nonholonomic deformation found for the KdV equation is extended to the mKdV equation and generalized to the AKNS system. For the deformed mKdV equation we find a matrix Lax pair, a novel two-fold integrable hierarchy and exact N-soliton solutions exhibiting unusual accelerating motion. We show that both the deformed KdV and mKdV systems possess infinitely many gener...

Wave group dynamics is studied in the framework of the extended Korteweg-de Vries equation. The nonlinear Schrodinger equation is derived for weakly nonlinear wave packets, and the condition for modulational instability is obtained. It is shown that wave packets are unstable only for a positive sign of the coe cient of the cubic nonlinear term in the extended Korteweg-de Vries equation, and for...

The bi-Hamiltonian structure is established for the perturbation equations of KdV hierarchy and thus the perturbation equations themselves provide also examples among typical soliton equations. Besides, a more general bi-Hamiltonian integrable hierarchy is proposed and a remark is given for a generalization of the resulting perturbation equations to 1 + 2 dimensions. Perturbation theory is the ...

In this paper implementations of three numerical schemes for the numerical simulation of the complex modi ed Korteweg de Vries CMKdV equation are reported The rst is an integrable scheme derived by methods related to the Inverse Scattering Transform IST The second is derived from the rst and is called the local IST scheme The third is a standard nite di erence scheme for the CMKdV equation Trav...

In this letter, a Painlevé integrable coupled KdV equation is proved to be also Lax integrable by a prolongation technique. The Miura transformation and the corresponding coupled modified KdV equation associated with this equation are derived. © 2010 Published by Elsevier Ltd

Transfer RNA's role in decoding the genome is critical to the accuracy and ef®ciency of protein synthesis. Though modi®ed nucleosides were identi®ed in RNA 50 years ago, only recently has their importance to tRNA's ability to decode cognate and wobble codons become apparent. RNA modi®cations are ubiquitous. To date, some 100 different posttranslational modi®cations have been identi®ed. Modi®cat...

We study the relation between the centro-affine geometry of starshaped planar curves and the projective geometry of parametrized maps into RP. We show that projectivization induces a map between differential invariants and a bi-Poisson map between Hamiltonian structures. We also show that a Hamiltonian evolution equation for closed star-shaped planar curves, discovered by Pinkall, has the Schwa...