In this paper we propose a powerful modi®cation of Adomian decomposition method that will accelerate the rapid convergence of the series solution. The validity of the modi®ed technique is veri®ed through illustrative examples. In all cases of di€erential and integral equations, we obtained excellent performance from the modi®ed algorithm. The modi®cation could lead to a promising approach for m...

In this paper, using the Lie group analysis method, we study the invariance properties of the time fractional fifth-order KdV equation. A systematic research to derive Lie point symmetries to time fractional fifth-order KdV equation is performed. In the sense of point symmetry, all of the vector fields and the symmetry reductions of the fractional fifth-order KdV equation are obtained. At last,...

In this paper, we derive a Bäcklund transformation for the supersymmetric Kortwegde Vries equation. We also construct a nonlinear superposition formula, which allows us to rebuild systematically for the supersymmetric KdV equation the soliton solutions of Carstea, Ramani and Grammaticos. The celebrated Kortweg-de Vries (KdV) equation was extended into super framework by Kupershmidt [3] in 1984....

In this paper, we derive a Bäcklund transformation for the supersymmetric Korteweg-de Vries equation. We also construct a nonlinear superposition formula, which allows us to rebuild systematically for the supersymmetric KdV equation the soliton solutions of Carstea, Ramani and Grammaticos. The celebrated Korteweg-de Vries (KdV) equation was extended into super framework by Kupershmidt [3] in 19...

We study a generalization of the hierarchy of mKdV equations (modi-ed KdV), which forms an integrable system. This generalization is based on a Lax operator associated to the equations, with principal components of degrees between ?3 and 0. The main result of the study is the com-mutation of the classical integrals of motion. For that purpose, one can construct an isomorphism between the space ...

We construct a one-parameter family of N=3 supersymmetric extensions of the KdV equation as a Hamiltonian flow on N=3 superconformal algebra and argue that it is non-integrable for any choice of the parameter. Then we propose a modified N=3 super KdV equation which possesses the higher order conserved quantities and so is a candidate for an integrable system. Upon reduction to N=2, it yields th...

A study is presented of fully discretized lattice equations associated with the KdV hierarchy. Loop group methods give a systematic way of constructing discretizations of the equations in the hierarchy. The lattice KdV system of Nijhoff et al. arises from the lowest order discretization of the trivial, lowest order equation in the hierarchy, bt = bx. Two new discretizations are also given, the ...

A micromechanical technique for measuring solution pH using modi®ed silicon (SiO2) and silicon nitride (Si3N4) microcantilevers is described. As the modi®ed surface of the cantilever accumulates charge proportional to the pH of the surrounding liquid, the cantilever undergoes bending due to the differential surface stress. Results are presented for chemically modi®ed (4-aminobutyltriethoxysilan...

In this paper, we consider multi-component generalizations of the Hirota–Satsuma coupled Korteweg–de Vries (KdV) equation. By introducing a Lax pair, we present a matrix generalization of the Hirota–Satsuma coupled KdV equation, which is shown to be reduced to a vector Hirota–Satsuma coupled KdV equation. By using Hirota's bilinear method, we find a few soliton solutions to the vector Hirota–Sa...