We develop a Fourier–Galerkin spectral technique for computing the stationary solutions of 2D generalized wave equations. To this end a special complete orthonormal system of functions in L2(−∞,∞) is used for which product formula is available. The exponential rate of convergence is...

The coupled nonlinear Schrödinger equation models several intersting physical phenomena. It presents a model equation for optical fiber with linear birefringence. In this paper, we present a linearly implicit conservative method to solve this equation. This method is second order accurate in...

A justified modification of the real part of the complex non-linearity of a Schrödinger equation, recently proposed G. Kaniadakis, Phys. Rev. A 55 (1997) 941], allows us to obtain a new canonical quantum system obeying an exclusion–inclusion principle. The soliton solutions of this new...

Surface diffusion (SD) is a really ubiquitous phenomenon playing a highly important part in a wealth of natural and technological processes. The effect of SD is to move surface atoms, molecules and clusters and allow them to assemble into some desirable configurations or, vise versa, to destroy...

The nonlinear Klein–Gordon equation with a different potential that satisfies the degeneracy properties discussed in this paper possesses solitonic solutions that interact with long-range forces. We generalize the Ginzburg–Landau equation in such a way that the topological defects supported...

We consider elastic grains which repel upon contact according to the Hertz potential V=aδn,n2, where δ is the overlap between adjacent grains and report numerical and analytical studies for the case of a 1-D chain of spherical grains to show that an impulse initiated at an end of a chain of...

We show that soliton interaction with finite-width inhomogeneities can activate a great number of soliton internal modes. We obtain the exact stationary soliton solution in the presence of inhomogeneities and solve exactly the stability problem. We present a Karhunen–Loève analysis of the...