Taimanov's evolution of conformally parametrized surfaces in Euclidean space by the modi ed Novikov-Veselov equation is interpreted here (in the revolution case) using hyperbolic geometry and B acklund transformations for curves.

In this work we apply an extended hyperbolic function method to solve the nonlinear family of third order Korteweg de-Vries (KdV) equations, namely, the KdV equation, the modified KdV (mKdV) equation, the potential KdV (pKdV) equation, the generalized KdV (gKdV) equation and gKdV with two power nonlinearities equation. New exact travelling wave solutions are obtained for the KdV, mKdV and pKdV ...

Suppose that a consistent one-step numerical method of order r is applied to a smooth system of ordinary differential equations. Given any integer m > 1, the method may be shown to be of order r + m as an approximation to a certain modi"ed equation. If the method and the system have a particular qualitative property then it is important to determine whether the modi"ed equations inherit this pr...

The equivalent, second equivalent and (simply) modi®ed equations for the implicit midpoint rule are shown to be asymptotically equivalent in the sense that an asymptotic analysis of these equations with the time step size as small parameter yields exactly the same results; for linear problems with constant coecients, they are also equivalent to the original ®nite di€erence scheme. Straightforw...

Soliton interactions for the extended Korteweg-de Vries (KdV) equation are examined. It is shown that the extended KdV equation can be transformed (to its order of approximation) to a higher-order member of the KdV hierarchy of integrable equations. This transformation is used to derive the higher-order, two-soliton solution for the extended KdV equation. Hence it follows that the higher-order ...

  In this paper, we establish exact solutions for the time-fractional Klein-Gordon equation, and the time-fractional Hirota-Satsuma coupled KdV system. The He’s semi-inverse and the Kudryashov methods are used to construct exact solutions of these equations. We apply He’s semi-inverse method to establish a variational theory for the time-fractional Klein-Gordon equation, and the time-fractiona...

in this paper, modication of the optimal homotopy asymptotic method (moham) is appliedupon singular initial value lane-emden type equations and results are compared with the available exactsolutions. the modied algorithm give the exact solution for dierential equations by using one iterationonly.

We investigate simulations of exact solutions of the stochastic Dr. Herman Numerical Realizations of Solutions f the Stochastic KdV Equation Exact Solution of Stochastic KdV Wadati 1983 The One Soliton Solution Under Noise Statistical Averages The Exact Solution for < u(x, t) > via the Diffusion Equation Solving the Diffusion Equation The Damped Stochastic KdV Asymptotics Numerical Simulation o...

The connection between supersymmetric quantummechanics and the Kortewegde Vries (KdV) equation is discussed, with particular emphasis on the KdV conservation laws. It is shown that supersymmetric quantum mechanics aids in the derivation of the conservation laws, and gives some insight into the Miura transformation that converts the KdV equation into the modified KdV equation. The construction o...

in the real world there are groups which composed of independent units. the conventional data envelopment analysis(dea) model treats groups as units, ignoring the operation of individual units within each group.the current paper, investigates parallel system network approach proposed by kao and modifies it. as modied kao&apos; model is more eligible to recognize ecient groups, a new ranking m...