CONTENTS -- Preface -- Soliton Excitations and Periodic Waves without Dispersion Relation in (2 + 1)-Dimensional Dispersive Long Wave Equation -- 1. Introduction -- 2. Extended Painleve Expansions -- 3. Periodic Solutions of the DLWE -- 4. Summary and Discussions -- References -- Global Bifurcation from the Eigenvalues of Some Semilinear Biharmonic Equations -- 1. Introduction -- 2. The Linearized Problem -- 3. Global Bifurcation Results for the Biharmonic Operator -- References -- The Multisoliton Solutions of the KP Equation with Self-consistent Sources -- 1. Introduction -- 2. The KP Equation with Self-consistent Sources -- 3. Hirota Form's Solution -- 4. Wronskian Form's Solution -- References -- A Direct Extension of Lie Algebra An-1 -- 1. Introduction -- 2. Hierarchy of Evolution Equations Associated with Lie Algebra gl(2 C) -- References -- On Gauge-gravity Correspondence and Open-closed String Duality -- 1. Introduction -- 2. Large N and Strings -- 3. Gauge-Gravity Correspondence for Less Supersymmetries -- 4. Confinement -- References -- Integrable Semi-discretizations of the AKNS Equation and the Hirota-Satsuma Equation -- 1. Introduction -- 2. Integrable Semi-discretization of the AKNS Equation -- 4. An Integrable Differential-Difference Equation for (5) -- 5. Another Integrable Differential-Difference Equation for (5) -- 6. Conclusion and Discussion -- References -- Differential Equations and Conformal Field Theories -- 1. Introduction -- 2. Conformal Field Theories -- 3. Differential Equations and Chiral Genus-Zero Correlation Functions -- 4. Differential Equations and Chiral Genus-One Correlation Functions -- References -- Lie Symmetries for Lattice Equations -- 1. Introduction -- References.

Multi-scale Reduction for Differential Difference Equations and Integrability -- 1. Introduction -- 2. Multiscale reduction for PDE -- 3. Multiscale reduction for DDE -- 4. Study of the NDNLS -- 5. Conclusions -- References -- p-Harmonic Maps with Applications -- 1. Introduction -- 2. Existence Theory -- 3. Uniqueness -- 4. Regularity -- 5. Solutions to Dirichlet Problem -- 6. n-Energy Identities -- 7. Representing Homotopy Classes by p-Harmonic Maps -- 8. A Bernstein-type Theorem -- 9. Isoperimetric Inequalities and Sphere Theorems -- References -- The Infinitely Many Conservation Laws of the Lax Integrable Differential-difference Systems -- 1. Introduction -- 2. The CLs for the (1+1)-Dimensional Differential- Difference Systems -- 3. The CLs for the High Dimensional Differential- Difference Systems -- 4. Conclusions -- References -- Quivers and Hopf Algebras -- 1. Path Algebras and Path Coalgebras -- 2. Cotensor Product Coalgebras -- 3. Hopf Bimodules over Group Algebras -- 4. Hopf Quivers -- 5. Hopf Structures on Path Coalgebras -- References -- Theory of Bidirectional Solitons on Water -- 1. Introduction -- 2. The Algebraic Properties of the Model Equation (3) and its Related Equivalent Equations -- 3. The Darboux Transformation of the BK System -- 4. The Darboux Transformation of the AKNS System -- 5. The Mechanics of Soliton Interaction -- 6. Conclusion -- References -- A Finite Dimensional Integrable System Associated with BKK Soliton Equation -- 1. Introduction -- 2. BKK Hierarchy -- 3. The Finite Dimensional Hamiltonian System -- 4. Some Solutions of the System -- References -- The Novel N-Soliton Solutions of Equation for Shallow Water Waves -- 1. Introduction -- 2. Exact N-soliton Solutions of Equation (1) -- 3. Novel N-soliton of Equation (2) -- 4. The Singularities of the Solution for Equations -- References.

A New Integrable Hierarchy and its Expansive Integrable Model -- 1. Introduction -- 2. A New Integrable Hierarchy -- 3. A New Loop Algebra and Expanding Integrable Model of the Integrable System (9) or (13) -- References -- Extremal Functions of Sobolev-Poincare Inequality -- 1. Introduction -- 2. Outline of the Proofs -- References -- List of the Participants.