Breaking solitons in 2+1-dimensional integrable equations

CONTENTS Introduction Chapter I. Integrable equations with attractors § 1. Algebraic construction of differential equations with attractors § 2. Dynamical systems with attractors § 3. 1+1-dimensional integrable equations Chapter II. Breaking solitons in 2+1-dimensional integrable equations § 1. 2+1-dimensional integrable equation § 2. Basic lemma § 3. Breaking solitons and N-soliton solutions § 4. The second 2+1-dimensional integrable equation § 5. Connection with the Kadomtsev-Petviashvili equation § 6. Dynamics of the poles of meromorphic solutions § 7. Integrable two-dimensionalization of the Burgers equation and dynamics of singularities § 8. 3+1-dimensional integrable equation § 9. The third 2+1-dimensional integrable equation § 10. Application of the Painlevé method Chapter III. 2+1-dimensional modified integrable equation § 1. 2+1-dimensional modified equation § 2. Countable set of conservation laws § 3. Lax representation for the 2+1-dimensional modified equation (1.5) § 4. Lax representation for 2+1-dimensional equations (1.5) and (1.6) § 5. Lax representation with a Hermitian operator L § 6. Breaking solitons § 7. Evolution of scattering data § 8. Integrable extension of the KdV equation with the fourth-order Lax operator L § 9. 3+1-dimensional complex integrable equation § 10. Integrable complexifications of the KdV and MKdV equations Chapter IV. Breaking solutions in continual limits of dynamical systems § 1. Continual limits of the Toda lattice and its two-dimensionalization § 2. Continual limits of the Fermi-Pasta-Ulam systems and their two-dimensionalization References