This paper considers the stability of soliton-like pulses propagating in nonlinear optical bers with periodically-spaced phase-sensitive ampli ers, a situation where the averaged pulse evolution is governed by a fourth-order nonlinear di usion equation similar to the KuramotoSivashinsky or Swift-Hohenberg equations. A bifurcation and stability analysis of this averaged equation is carried out, ...

Realistic behavior of deformable objects is essential for many applications such as simulation for surgical training. Existing techniques of deformable modeling for real time simulation have either used approximate methods that are not physically accurate or linear methods that do not produce reasonable global behavior. Nonlinear finite element methods (FEM) are globally accurate, but conventio...

Using a method of expansion similar to Chapman Enskog expansion, a new formal perturbation scheme based on high frequency approximation has been constructed. The scheme leads to an eikonal equation in which the leading order amplitude appears. The transport equation for the amplitude has been deduced with an error O(ǫ2) where ǫ is the small parameter appearing in the high frequency approximatio...

Landen formulas, which connect Jacobi elliptic functions with different modulus parameters, were first obtained over two hundred years ago by making a suitable quadratic transformation of variables in elliptic integrals. We obtain and discuss significant generalizations of the celebrated Landen formulas. Our approach is based on some recently obtained periodic solutions of physically interestin...

In this paper we study Lie symmetries, Kac-Moody-Virasoro algebras, similarity reductions and particular solutions of two different recently introduced (2+1)-dimensional nonlinear evolution equations, namely (i) (2+1)-dimensional breaking soliton equation and (ii) (2+1)-dimensional nonlinear Schrödinger type equation introduced by Zakharov and studied later by Strachan. Interestingly our studie...

We consider the long-standing problem of predicting the hierarchical clustering amplitudes Sp in the strongly non-linear regime of gravitational evolution. N-body results for the nonlinear evolution of the bispectrum (the Fourier transform of the three-point density correlation function) suggest a physically motivated ansatz that yields the strongly non-linear behavior of the skewness, S3, star...

A new algorithm is developed for the enforcement of constraints within the framework of nonlinear, flexible multibody system modeled with the finite element approach. The proposed algorithm exactly satisfies the constraints at the displacement and velocity levels, and furthermore, it achieves nonlinear unconditional stability by imposing the vanishing of the work done by the constraint forces w...

A large class of physically important nonlinear and nonhomogeneous evolution problems, characterized by advection-like and diffusion-like processes, can be usefully studied by a time-differential form of Kolmogorov’s solution of the backward-time Fokker-Planck equation. The differential solution embodies an integral representation theorem by which any physical or mathematical entity satisfying ...

Using $$\Gamma $$ -convergence arguments, we construct a nonlinear membrane-like Cosserat shell model on curvy reference configuration starting from geometrically nonlinear, physically linear three-dimensional isotropic model. Even if the theory is of order O(h) in thickness h, by comparison to membrane models proposed classical elasticity, beside change metric, still capable capturing transver...

Abstract : In a previous work [1], three of us have studied a nonlinear parabolic equation arising in the mesoscopic modelling of concentrated suspensions of particles that are subjected to a given time-dependent shear rate. In the present work we extend the model to allow for a more physically relevant situation when the shear rate actually depends on the macroscopic velocity of the fluid, and...