Title Nonlinear Systems and Their Remarkable Mathematical Structures : Volume 3, Contributions from China

Published Milton : CRC Press LLC, 2021

Click on the following:
ProQuest Ebook Central

Copies

Description 1 online resource (510 p.) Contents Cover -- Half Title -- Title Page -- Copyright Page -- Contents -- Preface -- The Authors -- PART A: Integrability and Symmetries -- A1. BKP hierarchy and modified BKP hierarchy -- 1. Introduction -- 2. BKP hierarchy and neutral Fermions -- 3. Constrained BKP hierarchy -- 4. Modified BKP hierarchy -- A2. Elementary introduction to the direct linearisation of integrable systems -- 1. Introduction -- 2. Infinite matrices and vectors -- 3. General theory of the direct linearisation -- 4. Discrete and continuous KP hierarchies -- 5. Concluding remarks -- A3. Discrete Boussinesq-type equations -- 1. Introduction -- 2. DBSQ-type equations -- 3. Two- and one-component forms -- 4. Continuum limits -- 5. Lax pairs -- 6. Bilinear structures of DBSQ-type equations -- 7. Conclusions -- Appendix A: Triply shifted variables from CAC -- A4. The study of integrable hierarchies in terms of Liouville correspondences -- 1. Introduction -- 2. The Liouville correspondences for the CH and mCH integrable hierarchies -- 3. Liouville correspondences for the Novikov and Degasperis Procesi integrable hierarchies -- 4. Liouville correspondences for multi-component integrable hierarchies -- 5. The Liouville correspondences for the dual Schrodinger integrable hierarchy and the (defocusing) mKdV hierarchy -- A5. Darboux transformations for supersymmetric integrable systems: A brief review -- 1. Introduction -- 2. Darboux transformations -- 3. Discrete systems -- 4. Continuum limits of the discrete systems -- 5. List of supersymmetric integrable equations -- A6. Nonlocal symmetries of nonlinear integrable systems -- 1. Introduction -- 2. Nonlocal symmetries in integrable systems -- 3. Nonlocal symmetries and nonlinearizations -- 4. Nonlocal symmetries and self-consistent sources -- 5. Localizations of nonlocal symmetries -- 6. Summary and discussions A7. High-order soliton matrix for an extended nonlinear SchrŁodinger equation -- 1. Introduction -- 2. Inverse scattering theory for ENLS equation -- 3. N-Soliton Solutions -- 4. Soliton matrix for high-order zeros -- 5. Dynamics of high-order solitons in the ENLS equation -- 6. Conclusion -- A8. Darboux transformation for integrable systems with symmetries -- 1. Introduction -- 2. Darboux transformation for general 1+1 dimensional Lax pairs -- 3. Darboux transformation for Lax pairs with unitary symmetry -- 4. Darboux transformation for MKdV equation -- 5. Darboux transformation for 2D D(2)l+1 Toda equation -- 6. Discussion -- A9. Frobenius manifolds and Orbit spaces of reflection groups and their extensions -- 1. Introduction -- 2. Frobenius manifolds and Reection groups -- 3. Frobenius manifolds and Extended affine Weyl groups -- 4. Jacobi groups and their extensions -- PART B: Algebraic, Analytic and Geometric Methods -- B1. On finite Toda type lattices and multipeakonsof the Camassa-Holm type equations -- 1. Background -- 2. Main results -- 3. Conclusion and discussion -- B2. Long-time asymptotics for the generalized coupled derivative nonlinear Schrodinger equation -- 1. Introduction -- 2. The Riemann-Hilbert proble -- 3. Long-time asymptotic behavior -- B3. Bilinearization of nonlinear integrable evolution equations: Recursion operator approach -- 1. Introduction -- 2. Bilinear form of the AKNS hierarchy -- 3. Bilinear form of the NLS hierarchy -- 4. Bilinear form of the Boussinesq hierarchy -- 5. Bilinear form of Levi hierarchy -- 6. Bilinear form of the Yajima-Oikawa hierarchy -- 7. Conclusion and discussions -- Appendix A: Bilinear Identities -- Appendix B: Bilinear Backlund transformations for the Boussinesq, Sawada-Koterra, Ito, Ramani, Lotka-Volterra and negative Volterra hierarchies B4. Rogue wave patterns and modulational instability in nonlinear Schrodinger hierarchy -- 1. Introduction -- 2. Vector NLS equations and Hirota equations -- 3. Breathers, rogue waves and W-shape solitons -- 4. Vector breathers and rogue waves -- 5. Discussions and conclusions -- B5. Algebro-geometric solutions to the modified Blaszak-Marciniak lattice hierarchy -- 1. Introduction -- 2. The mBM hierarchy -- 3. The stationary Baker-Akhiezer function -- 4. Algebro-geometric solutions to the stationary mBM hierarchy -- 5. Algebro-geometric solutions of the time-dependent mBM hierarchy -- B6. Long-time asymptotic behavior of the modified Schrodinger equation via @-steepest descent method -- 1. Introduction -- 2. Conjugation -- 3. Mixed -Riemann-Hilbert Problem -- 4. Model RHP and pure @-problem -- 5. The outer model Riemann-Hilbert problem -- 6. Local model RHP near z0 -- 7. The small norm RHP for E(z) -- 8. @ Problem -- 9. Long-time asymptotics for modified NLS equation -- B7. Two hierarchies of multiple solitons and soliton moleculesof (2+1)-dimensional Sawada-Kotera type equation -- 1. Introduction -- 2. New bilinearizations of 2DSK equation (1.1) -- 3. Multiple solition and soliton molecule solutions -- 4. Concluding remarks -- B8. Dressing the boundary: exact solutions of soliton equations on the half-line -- 1. Introduction -- 2. Notions of integrable boundary conditions -- 3. Dressing the boundary -- 4. Dressing the boundary as an inverse scattering transform -- 5. Concluding remarks -- B9. From integrable spatial discrete hierarchy tointegrable nonlinear PDE hierarchy -- 1. Introduction -- 2. From integrable spatial discrete KdV hierarchy to KdV hierarchy -- 3. From integrability of spatial discrete Hirota equation to integrability of Hirota equation -- 4. Conclusions Notes Description based upon print version of record Subject Differential equations, Nonlinear. Form Electronic book Author Zhang, Da-jun ISBN 9781000423266 1000423263

  Permalink