We show that the following geometric properties of the motion of discrete and continuous curves select integrable dynamics: i) the motion of the curve takes place in the N dimensional sphere of radius R, ii) the curve does not stretch during the motion, iii) the equations of the dynamics do not depend explicitly on the radius of the sphere. Well known examples of integrable evolution equations,...

We study a two-dimensional integrable generalization of the Kaup-Kupershmidt equation, which arises in various problems in mathematical physics. Exact solutions are obtained using the Lie symmetry method in conjunction with the extended tanhmethod and the extended Jacobi elliptic functionmethod. In addition to exact solutions we also present conservation laws which are derived using the multipl...

Abstract In recent years, new properties of space-time duality in the Hamiltonian formalism certain integrable classical field theories have been discovered and led to their reformulation using ideas from covariant theory: this sense, nature r -matrix structure was unravelled. Here, we solve open question extending these results a whole hierarchy. We choose Ablowitz–Kaup–Newell–Segur (AKNS) To ...

We present perturbation theory based on the inverse scattering transform method for solitons described by an equation with linear dispersion law $\ensuremath{\omega}\ensuremath{\sim}1/k$, where $\ensuremath{\omega}$ is frequency and $k$ wave number, cubic nonlinearity. This equation, first suggested Davydova Lashkin describing dynamics of nonlinear short-wavelength ion-cyclotron waves in plasma...

The study of integrable systems is one important topics both in physics and mathematics. However, traditional studies on are usually restricted (1+1) (2+1) dimensions. main reasons come from the fact that high-dimensional extremely rare. Recently, we found a large number high dimensional can be derived low ones by means deformation algorithm. In this paper, Kaup-Newell (KN) system extended to (...