目录 非线性科学丛书出版说明 前言 第1章浅水槽中的孤波与孤子 §1波、水表面波和色散… 1.1波和色散… 1113 §1.2流体力学方程… ● §1.3线性小振幅水波… … 5 2孤波的发现… 7 §3孤子的相互作用 …13 ↓守恒定律 …17 解dV方程初值问题的反散射方法 19 6水槽中KdV孤子实验… …26 7kdv方程的应用及其推广 ………28 第2章深水槽中的包络孤波… …30 §8深水中的斯托克斯波和边带不稳定性……30 §9NLS方程与斯托克斯波的失稳…33 §10NLS方程初值问题与实验结果…36 11NLS方程与周期回归现象 …41 12束缚态与多(阶)极(点)解 …44 §13暗孤波(包络洞孤波)… 46 第3章参量激发驻孤波 ……49
§14参量共振… 4 §15参量激发驻孤波…54 16 PDNIS方程和驻孤波解…57 17椭圆驻波解与“反向孤子对…61 §18扭结表面波… 66 19界面驻孤波… . 第4章法拉第孤子间的周期性往复运动… …70 20法拉第孤子的周期性往复运动…70 21描述法拉第孤子周期性往复运动的方程…73 22一对“同相孤子的相互往复振荡79 23边界条件及讨论 3 第5章参量激发水表面波的动力学行为… …85 24驻孤波的稳定区和分岔混沌现象85 25 PDNLS方程驻孤波解稳定性分析S 26pdnS方程的动力学行为 …9 §27存在问题与展望95 附录AKdV方程的推导和它的永形波解98 附录B慢调制深水波中的NLS方程104 附录 PDNLS方程的推导… …113 附录D参量激励下界面波方程 ……118 参考文献 120
Contents Prefab Chapter I The solitary waves and solitons in shallow water trough §1 Waves, water waves and dispersion……………1 N2 The discovery of solitary waves…………………7 §3 The interaction of solitons……………… N4 Conservation laws… 17 85 The inverse scattering method for solving the initial-value problems of KdV equation .... 19 86 The experiments on the KdV solitons in water trough…………26 §7 Applications of KdⅤ equation and its generalization…28 Chapter 2 The envelope solitons in deep water trough………………………30 &8 The stokes wave on deep water and the side- band instability…………30 89 NLS equation and the intability of Stokes waves…·…33 8 10 The initial-value problems of
equation and the experimental results ee e.. 36 811 NLS equation and the phenomena of recurrence························.············ 812 The bounded states and the multiple pole solutions………………………………44 $13 Dark solitary wave (envelope-hole solit Chapter 3 ParametricaLly excited standing solitary waves……·…………49 §14 Paramatrical resonance……………49 8 15 Parametrically excited standing solitary wave s54 816 PDNIS equation and the standing solitary wave solution…………… 817 The cnoidal standing wave solution and the so calles"a pair of solitons of opposite polarity ·自·非·····.········,··;·.●··,·s.s·当非·a §18 The kink surface wave………………66 §19 The standing solitary wave on interface………68 Chapter 4 The mutual oscillatory(back and forth) motion of Faraday solitons………70 8 20 The mutual oscillatory (back and forth) motion of Faraday solitons…………………70 8 21 The equation of the Faraday solitons with mutual oscillatory( baek and forth) motion……73 8 22 The mutual oscillatory motion of two
solitons with the same polarity". s23 boundary condition and discussion……83 Chaper 5 The dynamic behaviors of parametrically excited water waves……85 8 24 The stable parametrical regions of g solitary wave and the phenomena of bifurcation and cha 85 8 25 Stability analysis of the standing solitary wave solution of PDNlS equation 26 The dynamic behaviors of PDNLS equation……93 8 27 Unsolved problems and prospects 95 Appendix A Derivation of Kdv equation and its solutions of permanent form waves 98 Appendix B NLs equation of slow-modulating deep water waves…………104 Appendix C Derivation of PDNLS equation……113 Appendix d Equations of parametrically excited interface wave 118 References……120