Solitary waves in a one-dimensional chain of atoms {qj}j∈Z are investigated. The potential energy is required to be monotone and grow super-quadratically. The existence of solitary waves with a prescribed asymptotic strain is shown under certain assumptions on the asymptotic strain and the wave speed. It is demonstrated the invariance of the equations allows one to transform a system with non-c...

We demonstrate the existence of dynamically stable multihump solitary waves in polaron-type models describing interaction of envelope and lattice excitations. In comparison with the earlier theory of multihump optical solitons (see Phys. Rev. Lett. 83 (1999) 296), our analysis reveals a novel physical mechanism for the formation of stable multihump solitary waves in nonintegrable multi-componen...

In this paper we study the structure of the manifold of solitary waves in some deformations of SO(2) symmetric two-component scalar field theoretical models in two-dimensional Minkowski space. The deformation is chosen in order to make the analogous mechanical system Hamilton-Jacobi separable in polar coordinates and displays a singularity at the origin of the internal plane. The existence of t...

We demonstrate that, in contrast with what was previously believed, multihump solitary waves can be stable. By means of linear stability analysis and numerical simulations, we investigate the stability of twoand three-hump solitary waves governed by incoherent beam interaction in a saturable medium, providing a theoretical background for the stability of the experimental results reported by Mit...

We consider the stability of solitary waves of a class of 5th order KdV equations. It is known that their stability is determined by the second derivative of a function of the wave speed d(c). We perform a detailed investigation of the properties of this function, both analytically and numerically. For a class of homogeneous nonlinearities, we precisely determine the regions of wave speeds for ...

We present a phenomenological approach to dispersion in nonlinear elasticity. A simple, thermomechanically sound, constitutive model is proposed to describe the (non-dissipative) properties of a hyperelastic dispersive solid, without recourse to a microstructure or a special geometry. As a result, nonlinear and dispersive waves can travel in the bulk of such solids, and special waves emerge, so...

We study asymptotic stability of solitary wave solutions in the one-dimensional Benney-Luke equation, a formally valid approximation for describing two-way water wave propagation. For this equation, as for the full water wave problem, the classic variational method for proving orbital stability of solitary waves fails dramatically due to the fact that the second variation of the energy-momentum...

In applications, solitary-wave solutions of semilinear elliptic equations u + g(u; ru) = 0 (x; y) 2 IR in innnite cylinders frequently arise as travelling waves of parabolic equations. As such, their bifurcations are an interesting issue. Interpreting elliptic equations on innnite cylinders as dynamical systems in x has proved very useful. Still, there are major obstacles in obtaining, for inst...