دانلود کتاب Nonlinear Systems and Their Remarkable Mathematical Structures: Volume 1

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