A new method of finding the periodic solutions for the equations integrable within the
framework of the AKNS scheme is reviewed. The approach is a modification of the known …

Publisher Summary This chapter describes polycnoidal waves, periodic waves as exact
imbricate series of solitons, and numerical boundary value algorithms for direct computation …

Let us consider a small domain II in the complex plane, ze II and an immersion F: II–» R" of II
into Euclidean space. It is well known that if F is a conformal parametrization of a surface …

The cubic nonlinear Schroedinger equation (NLS) describes the space-time evolution of
narrow-banded wave trains in one space and one time (1+ 1) dimensions. The richness of …

We revisit the exact thermodynamic description of the classical sine-Gordon field theory, a
well-known integrable model. We found that existing results in the literature based on the …

This book was written from lectures given to MSc students following the'Matter and
Radiation'course at the University of Grenoble I. Although magnetism and superconductivity …

The cubic Schrödinger equation (CSE)(iu t+ u xx±2‖ u‖ 2 u= 0) is a generic model
equation used in the study of modulational problems in one spatial dimension. The CSE is …

Abstract The known (2+ 1)-dimensional breaking soliton equation, the coupled KP equation
with three potentials and a new (3+ 1)-dimensional nonlinear evolution equation are …

We describe the integrable structure of solutions of the nonlinear Schrodinger (NLS)
equation under periodic and quasiperiodic boundary conditions. We focus on those aspects …

In this paper the homoclinic geometric structure of the integrable sine-Gordon equation
under periodic boundary conditions is developed. Specifically, focus is given to orbits …